Understanding Chaotic Dynamical Systems
From MaRDI portal
Publication:5325965
DOI10.1002/cpa.21468zbMath1305.37004OpenAlexW1967724736MaRDI QIDQ5325965
Publication date: 31 July 2013
Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/cpa.21468
Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02)
Related Items
Nonexistence of observable chaos and its robustness in strongly monotone dynamical systems ⋮ Sharpened dynamics alternative and its \(C^1\)-robustness for strongly monotone discrete dynamical systems ⋮ Map lattices coupled by collisions: hitting time statistics and collisions per lattice unit ⋮ Crisis of the chaotic attractor of a climate model: a transfer operator approach ⋮ Strange Attractors in a Three-Dimensional Autonomous Polynomial Equation ⋮ Equilibrium states for non-transitive random open and closed dynamical systems ⋮ Resonances in a chaotic attractor crisis of the Lorenz flow ⋮ Multiplicative ergodic theorems for transfer operators: Towards the identification and analysis of coherent structures in non-autonomous dynamical systems
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Dispersing billiards with moving scatterers
- Dynamics of periodically kicked oscillators
- Extensive escape rate in lattices of weakly coupled expanding maps
- The dynamics of the Hénon map
- Principles for the design of billiards with nonvanishing Lyapunov exponents
- The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
- Entropy formula for random transformations
- Generic hyperbolicity in the logistic family
- Ergodic theory of differentiable dynamical systems
- Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
- The ergodic theory of axiom A flows
- Statistical properties of dynamical systems with some hyperbolicity
- Recurrence times and rates of mixing
- Sinai-Bowen-Ruelle measures for certain Hénon maps
- From invariant curves to strange attractors
- Infinite-dimensional dynamical systems in mechanics and physics.
- Dynamics of quadratic polynomials. I, II
- Strange attractors in periodically-kicked limit cycles and Hopf bifurcations
- Stable ergodicity and julienne quasi-conformality
- SRB measures for partially hyperbolic systems whose central direction is mostly expanding
- Almost every real quadratic map is either regular or stochastic.
- Decay of correlations
- Limitations of perturbative techniques in the analysis of rhythms and oscillations
- On infinite-volume mixing
- SRB measures for partially hyperbolic systems whose central direction is mostly contracting
- Toward a theory of rank one attractors
- Limit theorems for locally perturbed planar Lorentz processes
- Lyapunov exponents, periodic orbits, and horseshoes for semiflows on Hilbert spaces
- A proof of the estimation from below in Pesin's entropy formula
- Bowen-Ruelle Measures for Certain Piecewise Hyperbolic Maps
- Chaotic attractors of relaxation oscillators
- Dynamical Processes on Complex Networks
- Gibbs measures for partially hyperbolic attractors
- An inequality for the entropy of differentiable maps
- Qualitative analysis of the periodically forced relaxation oscillations
- A Measure Associated with Axiom-A Attractors
- CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
- Billiards with polynomial decay of correlations
- Finding finite-time invariant manifolds in two-dimensional velocity fields
- Ergodic theory of chaos and strange attractors
- Deterministic Nonperiodic Flow
- Extensive bounds on the topological entropy of repellers in piecewise expanding coupled map lattices
- Lagrangian coherent structures and the smallest finite-time Lyapunov exponent
- Large deviations in non-uniformly hyperbolic dynamical systems
- Horseshoes in the forced van der Pol system
- Differentiable dynamical systems
- Dynamical systems with elastic reflections
- On Non-Linear Differential Equations of the Second Order: I. the Equation y¨ − k (1-y 2 )y˙ + y = b λk cos(λl + α), k Large
- Equilibrium states and the ergodic theory of Anosov diffeomorphisms
- A second order differential equation with singular solutions
- Strange attractors with one direction of instability