Ergodic theory of chaos and strange attractors

No abstract is available for this paper.

• Publication year

  1985

• Venue

  Reviews of Modern Physics

• Publication date

  1985-07-01

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1103/REVMODPHYS.57.617
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Ergodic properties of linear dynamical systems

  1987cited by this paper
• Invariant Manifolds, Entropy and Billiards: Smooth Maps With Singularities

  1986cited by this paper
• A multiplicative ergodic theorem for random transformations

  1985cited by this paper
• Repellers, semi-attractors, and long-lived chaotic transients

  1985cited by this paper
• Information Aspects of Strange Attractors

  1985cited by this paper
• Flows of stochastic dynamical systems: ergodic theory

  1985cited by this paper
• On the concept of attractor

  1985cited by this paper
• Computing the Kolmogorov entropy from time signals of dissipative and conservative dynamical systems.

  1985cited by this paper
• On Iterations of 1 - ax 2 on (- 1,1)

  1985cited by this paper
• The Static and Dynamic Invariants that Characterize Chaos and the Relations Between Them in Theory and Experiments

  1985cited by this paper
• Rotation numbers for diffeomorphisms and flows

  1985cited by this paper
• Neutron Scattering From a Convecting Nematic: Multicriticality, Multistability and Chaos

  1985cited by this paper
• The Physics of Chaos and Related Problems: Proceedings of the 59th Nobel Symposium

  1985cited by this paper
• Dimension of invariant measures for maps with exponent zero

  1985cited by this paper
• Liapounov exponents for the Kuramoto-Sivashinsky model

  1985cited by this paper
• Determining Lyapunov exponents from a time series

  1985cited by this paper
• Dimension, entropy and Lyapunov exponents in differentiable dynamical systems

  1984cited by this paper
• Nonchaotic Rayleigh-Bénard Convection with Four and Five Incommensurate Frequencies

  1984cited by this paper
• Fat baker's transformations

  1984cited by this paper
• L'ordre dans le chaos.

  1984cited by this paper
• The dimension of the maximal measure for a polynomial map

  1984cited by this paper
• Testing nonlinear dynamics

  1984cited by this paper
• Détermination de dimension d'attracteurs pour différents écoulements

  1984cited by this paper
• The metric entropy of diffeomorphisms

  1984cited by this paper
• Fractal Geometry of Nature

  1984cited by this paper
• Characteristic exponents for a viscous fluid subjected to time dependent forces

  1984cited by this paper
• On characteristic exponents in turbulence

  1984cited by this paper
• Order in chaos; Proceedings of the International Conference, Los Alamos, NM, May 24-28, 1982

  1983cited by this paper
• Observation of a strange attractor

  1983cited by this paper
• Hausdorff dimension for horseshoes

  1983cited by this paper
• Measuring the Strangeness of Strange Attractors

  1983cited by this paper
• Dimension of strange attractors : an experimental determination for the chaotic regime of two convective systems

  1983cited by this paper
• Estimation of the Kolmogorov entropy from a chaotic signal

  1983cited by this paper
• Are three-frequency quasiperiodic orbits to be expected in typical nonlinear dynamical systems

  1983cited by this paper
• Positive Liapunov exponents and absolute continuity for maps of the interval

  1983cited by this paper
• Crises, sudden changes in chaotic attractors, and transient chaos

  1983cited by this paper
• Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

  1983cited by this paper
• A proof of Pesin's stable manifold theorem

  1983cited by this paper
• Lyapounov exponents and stable manifolds for compact transformations

  1983cited by this paper
• C. Vidal, A. Pacault: (Eds.): Nonlinear Phenomena in Chemical Dynamics; Proceedings of an International Conference, Bordeaux, France; Vol. 12 aus: Springer Series in Synergetics, Springer-Verlag, Berlin, Heidelberg, New York 1981. 280 Seiten, Preis: DM 70,—

  1983cited by this paper
• The liapunov dimension of strange attractors

  1983cited by this paper
• Characteristic Exponents and Invariant Manifolds in Hilbert Space

  1982cited by this paper
• Dimension, entropy and Lyapunov exponents

  1982cited by this paper
• Noise in chaotic systems

  1982cited by this paper
• Experimental aspects of the transition to turbulence in Rayleigh-Bénard convection

  1982cited by this paper
• Large volume limit of the distribution of characteristic exponents in turbulence

  1982cited by this paper
• Partial regularity of suitable weak solutions of the navier‐stokes equations

  1982cited by this paper
• On computing the entropy of the Henon attractor

  1981cited by this paper
• Detecting strange attractors in turbulence

  1981cited by this paper
• Structure of mappings of an interval with zero entropy

  1981cited by this paper
• Small random perturbations of dynamical systems and the definition of attractors

  1981cited by this paper
• Strange Attractors, Chaotic Behavior, and Information Flow

  1981cited by this paper
• On the dimension of the compact invariant sets of certain non-linear maps

  1981cited by this paper
• Rayleigh-Benard Experiment in a Low Prandtl Number Fluid, Mercury

  1981cited by this paper
• Nonlinear Phenomena in Chemical Dynamics

  1981cited by this paper
• On the Hausdorff dimension of fractal attractors

  1981cited by this paper
• Absolutely continuous invariant measures for one-parameter families of one-dimensional maps

  1981cited by this paper
• Intermittency in nonlinear dynamics and singularities at complex times

  1981cited by this paper
• Capacity of attractors

  1981cited by this paper
• Some relations between dimension and Lyapounov exponents

  1981cited by this paper
• Some properties of absolutely continuous invariant measures on an interval

  1981cited by this paper
• Roads to turbulence in dissipative dynamical systems

  1981cited by this paper
• Topology of Chaos in a Chemical Reaction

  1981cited by this paper
• UNE EXPERIENCE DE RAYLEIGH-BENARD DE GEOMETRIE REDUITE ; MULTIPLICATION, ACCROCHAGE ET DEMULTIPLICATION DE FREQUENCES

  1980cited by this paper
• Universal properties of maps on an interval

  1980cited by this paper
• On the abundance of aperiodic behaviour for maps on the interval

  1980cited by this paper
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms

  1980cited by this paper
• Two remarks on the computer study of differentiable dynamical systems

  1980influential reference
• The transition to aperiodic behavior in turbulent systems

  1980cited by this paper
• MEASURES DESCRIBING A TURBULENT FLOW

  1980cited by this paper
• Iterated maps on the interval as dynamical systems

  1980cited by this paper
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms

  1979cited by this paper
• A proof of Oseledec’s multiplicative ergodic theorem

  1979cited by this paper
• The universal metric properties of nonlinear transformations

  1979cited by this paper
• Preturbulence: A regime observed in a fluid flow model of Lorenz

  1979cited by this paper
• On the Hénon transformation

  1979cited by this paper
• Ergodic theory of differentiable dynamical systems

  1979cited by this paper
• Gibbsian Distribution on the Lorenz Attractor

  1979cited by this paper
• Occurrence of strange AxiomA attractors near quasi periodic flows onTm,m≧3

  1978cited by this paper
• Isolated Invariant Sets and the Morse Index

  1978cited by this paper
• An inequality for the entropy of differentiable maps

  1978cited by this paper
• Quantitative universality for a class of nonlinear transformations

  1978cited by this paper
• Characteristic exponents and strange attractors

  1978cited by this paper
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY

  1977influential reference
• Ergodic Theory on Compact Spaces

  1976cited by this paper
• A two-dimensional mapping with a strange attractor

  1976cited by this paper
• Negatively invariant sets of compact maps and an extension of a theorem of Cartwright

  1976cited by this paper
• An equation for continuous chaos

  1976cited by this paper
• A MEASURE ASSOCIATED WITH AXIOM-A ATTRACTORS.

  1976cited by this paper
• Kolmogorov Entropy and Numerical Experiments

  1976cited by this paper
• Hausdorff dimension, orthogonal projections and intersections with planes

  1975cited by this paper
• Period Three Implies Chaos

  1975cited by this paper
• Ergodic theory of Axiom A flows

  1975cited by this paper
• Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms

  1975cited by this paper
• The Ergodic Theory of Axiom A Flows.

  1975cited by this paper
• The ergodic theory of AxiomA flows

  1975cited by this paper
• Diffeomorphisms with infinitely many sinks

  1974cited by this paper
• ON SMALL RANDOM PERTURBATIONS OF SOME SMOOTH DYNAMICAL SYSTEMS

  1974cited by this paper
• GIBBS MEASURES IN ERGODIC THEORY

  1972cited by this paper
• On the nature of turbulence

  1971cited by this paper

• Nonlinear motions induced by impacts from a rotor and stator under varying gravity coefficient

  2026cites this paper
• Predictability of complex systems

  2026cites this paper
• On the behavior of Linear Dependence, Smaller, and Generalized Alignment Indices in discrete and continuous chaotic systems

  2026cites this paper
• Skin Sympathetic Nerve Activity Complexity Predicts Sudden and Non-Sudden Cardiac Mortality in Heart Failure.

  2026cites this paper
• Geometry- and inertia-limited chaotic growth in classical many-body systems

  2026cites this paper
• Intelligence as high-dimensional coherence: The observable dimensionality bound and computational tractability

  2026cites this paper
• Nonlinear coupling dynamics within and between brains during romantic kissing as compared to joint passive tasks

  2026cites this paper
• Reverse Newhouse-Ruelle-Takens route to chaos and time-dependent Hamiltonian formulation of a generalized Muthuswamy-Chua system.

  2026cites this paper
• A phenomenological description of critical slowing down at period-doubling bifurcations

  2026cites this paper
• Inference of the size of nonlinear network systems from perceptible dynamics.

  2026cites this paper
• Wasserstein Geometry of Information Loss in Nonlinear Dynamical Systems

  2026cites this paper
• Spatiotemporal nonlinear behavior of cavitation inside the hydraulic regulating valve

  2026cites this paper
• Tracking Finite-Time Lyapunov Exponents to Robustify Neural ODEs

  2026cites this paper
• Correspondences in computational and dynamical complexity I

  2026cites this paper
• Lyapunov Spectral Analysis of Speech Embedding Trajectories in Psychosis

  2026cites this paper
• The Knowable Future: Mapping the Decay of Past-Future Mutual Information Across Forecast Horizons

  2026cites this paper
• Position: Why a Dynamical Systems Perspective is Needed to Advance Time Series Modeling

  2026influential citation
• Hyperbolicity and Southern Hemisphere Persistent Synoptic Events

  2025cites this paper
• Adjoint of Least Squares Shadowing: Existence, Uniqueness and Coarse Domain Discretization

  2025cites this paper
• Chaotic Dynamics of Spiral Bevel Gears

  2025cites this paper
• Classical vs quantum dynamics and the onset of chaos in a macrospin system

  2025cites this paper
• Topological Signatures of History-Dependent Invariants in the Lorenz System: Deterministic Probes of Lobe Dynamics

  2025cites this paper
• Prethermalization in Fermi-Pasta-Ulam-Tsingou chains.

  2025cites this paper
• Stability analysis, chaos control, and complex attractors in a modified Rossler model

  2025cites this paper
• Learning dissipation and instability fields from chaotic dynamics

  2025cites this paper
• How a responsive reproduction factor is determinant in a prey-predator dynamics: A numerical and analytical study in a discrete-time model.

  2025cites this paper
• Large Ensemble Simulations of Climate Models for Climate Change Research: A Review

  2025cites this paper
• Dimensions and entropies for an expansive homeomorphism

  2025cites this paper
• Inter-seasonal variability in predictability of South China seasonal precipitation

  2025cites this paper
• Complications of applying approximate entropy to heart rate variability to locate optimal complexity in children with attention deficit hyperactivity disorder

  2025cites this paper
• A Minimal Network of Brain Dynamics: Hierarchy of Approximations to Quasi-critical Neural Network Dynamics

  2025cites this paper
• Scale-dependent velocity fluctuations generated by molecular collisions

  2025cites this paper
• Final state sensitivity and fractal basin boundaries from coupled Chialvo neurons

  2025cites this paper
• Robustness of dynamical coupling between wintertime European weather extremes and the large-scale circulation

  2025cites this paper
• Low-noise analog Lorenz system on a credit-card-sized PCB with integrated ADC, display, and rechargeable battery

  2025cites this paper
• Multi Scale Analysis of Nifty 50 Return Characteristics Valuation Dynamics and Market Complexity 1990 to 2024

  2025cites this paper
• Ubiquity of Uncertainty in Neuron Systems

  2025cites this paper
• Scientific Machine Learning of Chaotic Systems Discovers Governing Equations for Neural Populations

  2025cites this paper
• Stochastic stability of physical measures in conservative systems

  2025cites this paper
• Role of structural properties in reliable prediction of CGLE via data assimilation

  2025cites this paper
• Trapping, chaos and averaging in bubbling AdS spaces

  2025cites this paper
• Constructing bifurcation diagram of reservoir computing

  2025cites this paper
• Random attractor and SRB measure for stochastic Hopf bifurcation under discretization

  2025cites this paper
• Non-linear dynamics of fluidized beds: Insights from coupled CFD-DEM simulations

  2025cites this paper
• On the relationship between equilibria and dynamics in large, random neuronal networks

  2025cites this paper
• An Introductory Guide to Koopman Learning

  2025cites this paper
• Approximate and Sample Entropy of the Center of Pressure During Unperturbed Tandem Standing: Effect of Altering the Tolerance Window

  2025cites this paper
• Unveiling synchronization transitions in networks of coupled oscillators through persistent homology of local structures

  2025cites this paper
• An improved approach for estimating the dimension of inertial manifolds in chaotic distributed dynamical systems via analysis of angles between tangent subspaces

  2025cites this paper
• Information theory and discriminative sampling for model discovery

  2025cites this paper
• Transient chaos and periodic structures in a model of neuronal early afterdepolarization.

  2025cites this paper
• Chaotic and fractal maps in higher-order derivative dynamical systems

  2025cites this paper
• Feature Entropy Recognition Based on Dual-Channel Multiscale 1DCNN Model for Intelligent Compound Fault Diagnosis of Bearings

  2025cites this paper
• KKL Observer Synthesis for Nonlinear Systems via Physics-Informed Learning

  2025cites this paper
• Phase space volume preserving dynamics for non-Hamiltonian systems

  2025cites this paper
• A simulation-supported thought experiment for measuring low-dimensional chaotic systems subjected to parameter drift.

  2025cites this paper
• Exploring Neimark-Sacker Bifurcation and Chaos Control in a Tri-species Discrete-Time Model

  2025cites this paper
• Predictability of temporal network dynamics in normal ageing and brain pathology

  2025cites this paper
• Ergodic Theory of Inhomogeneous Quantum Processes

  2025cites this paper
• Induced equilibria in the classical Lorenz system by means of a quadratic rational function

  2025cites this paper
• On the Topological Nature of the Butterfly Effect

  2025cites this paper
• Non-reciprocal interactions and high-dimensional chaos: comparing dynamics and statistics of equilibria in a solvable class of models

  2025cites this paper
• Geometric Hyperplane Intersection Solver: A Matrix-Inversion-Free Framework with Quantum-Neuroevolutionary Enhancements

  2025cites this paper
• A Simple Overview of Complex Systems and Complexity Measures

  2025cites this paper
• Locating Extremal Periodic Orbits for the Planar Circular Restricted Three Body Problem using Polynomial Sum-of-Squares Optimization

  2025cites this paper
• Rethinking Competition as a Non-Beneficial Mechanism in Economic Systems

  2025cites this paper
• Transformers Beyond Order: A Chaos-Markov-Gaussian Framework for Short-Term Sentiment Forecasting of Any Financial OHLC timeseries Data

  2025cites this paper
• Hyperchaos and complex dynamical regimes in N-dimensional neuron lattices

  2025cites this paper
• A dynamic view of some anomalous phenomena in SGD for over-parametrized neural networks

  2025cites this paper
• Reduced-order modelling of parameter-dependent systems with invariant manifolds: Application to Hopf bifurcations in follower force problems

  2025cites this paper
• Unifying concepts in information-theoretic time-series analysis

  2025cites this paper
• Non-uniqueness of stationary measures for stochastic systems with almost surely invariant manifolds

  2025cites this paper
• Distribution and recurrence in quasiperiodic and chaotic systems and the possible pathway to ergodicity

  2025influential citation
• The symbolic partition with generalized Koopman analysis

  2025cites this paper
• Delayformer: Spatiotemporal Transformation for Predicting High‐Dimensional Dynamics

  2025cites this paper
• A quantitative comparison of two methods for higher-order EEG microstate syntax analysis

  2025cites this paper
• pynamicalsys: A Python toolkit for the analysis of dynamical systems

  2025cites this paper
• Quasilinear dissipation estimates for strongly chaotic particle motion

  2025cites this paper
• Universal quantum melting of quasiperiodic attractors in driven-dissipative cavities

  2025cites this paper
• Estimating Free Parameters in Stochastic Oscillatory Models Using a Weighted Cost Function

  2025cites this paper
• A pseudospectral approach to rigorous numerical estimation of Ruelle resonances of transfer operators

  2025cites this paper
• A Novel Optical Transmitter With Chaotic Fingerprint for Identity Authentication in Physical-Layer Security of Optical Networks

  2025cites this paper
• Transparency versus Anderson localization in one-dimensional disordered stealthy hyperuniform layered media

  2025cites this paper
• Chaotic dynamics and fractal analysis of nonstandard Hamiltonian systems

  2025cites this paper
• HypER: Hyperbolic Echo State Networks for Capturing Stretch-and-Fold Dynamics in Chaotic Flows

  2025cites this paper
• Small-sample Bayesian error estimation for ergodic, chaotic systems of ordinary differential equations

  2025cites this paper
• Time series forecasting enhanced by Lyapunov exponent via attention mechanism

  2025cites this paper
• Geometry-aware reservoirs: Patch-wise Jacobian lifting with cross-patch couplings for piecewise-linear modelling of chaotic flows

  2025cites this paper
• Dynamical complexity in a discrete tri-trophic Rosenzweig–MacArthur system: Bifurcations, chaos and hybrid control

  2025cites this paper
• Riddled basin geometry sets fundamental limits to predictability and reproducibility in deep learning

  2025cites this paper
• How Far Can We Trust Chaos? Extending the Horizon of Predictability

  2025cites this paper
• K-M LLM-pro: Physics-guided cross-modal adaptation for fine-grained spatiotemporal trajectory classification

  2025cites this paper
• Some big issues with small noise limits in Markov decision processes

  2025cites this paper
• A Deep Learning Framework for Identifying Weakly Chaotic, Strongly Chaotic, Resonant and Non-resonant Orbits in the Generalized Kicked Rotator

  2025cites this paper
• Coupling and Parameter Estimation for a Discrete Single-Species Metapopulation Model

  2025influential citation
• Detection of Chatter in Machining Processes by the Multiscale Maximum Approximate Entropy and Continuous Wavelet Transform

  2025cites this paper
• Data-driven performance measures using global properties of attractors for testing black-box surrogate models of chaotic systems.

  2025cites this paper
• The Analytical Vision of Michael Turvey: A Review

  2025cites this paper
• Convergence Dynamics and Scaling Laws in the Dissipative Relativistic Kicked Rotator

  2025cites this paper
• Chaos Meets Attention: Transformers for Large-Scale Dynamical Prediction

  2025cites this paper