Quantitative quasiperiodicity

DOI10.1088/1361-6544/aa84c2zbMath1384.37009arXiv1601.06051OpenAlexW3038112447MaRDI QIDQ4597519

James A. Yorke, Evelyn Sander, Suddhasattwa Das, Yoshitaka Saiki

Publication date: 13 December 2017

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.06051

zbMATH Keywords

rotation numberquasiperiodicityHamiltonian systemBirkhoff ergodic theorem

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Related Items (16)

Lie group valued Koopman eigenfunctions ⋮ Birkhoff averages and rotational invariant circles for area-preserving maps ⋮ A numerical investigation of the pinning phenomenon in quasi-periodic Frenkel Kontorova model under an external force ⋮ Efficient and reliable algorithms for the computation of non-twist invariant circles ⋮ Accurate computations up to breakdown of quasi-periodic attractors in the dissipative spin-orbit problem ⋮ Distinguishing between regular and chaotic orbits of flows by the weighted Birkhoff average ⋮ Super convergence of ergodic averages for quasiperiodic orbits ⋮ Simply improved averaging for coupled oscillators and weakly nonlinear waves ⋮ Homoclinic Cycle Bifurcations in Planar Maps ⋮ Quasi-periodic orbits in Siegel disks/balls and the Babylonian problem ⋮ Effective bounds for the measure of rotations ⋮ Solving the Babylonian problem of quasiperiodic rotation rates ⋮ KAM quasi-periodic tori for the dissipative spin-orbit problem ⋮ Efficient and accurate KAM tori construction for the dissipative spin-orbit problem using a map reduction ⋮ Birkhoff averages and the breakdown of invariant tori in volume-preserving maps ⋮ Unpredictability in Hamiltonian systems with a hierarchical phase space

Uses Software

• Torcont

Cites Work

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• Quasi-periodic perturbations within the reversible context 2 in KAM theory
• Dynamical stability of quasi-periodic response solutions in planar conservative systems
• Fast iteration of cocycles over rotations and computation of hyperbolic bundles
• A proof of Oseledec's multiplicative ergodic theorem
• Frequency analysis of a dynamical system
• Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos
• Computation of derivatives of the rotation number for parametric families of circle diffeomorphisms
• Numerical computation of the asymptotic size of the rotation domain for the Arnold family
• Numerical computation of rotation numbers of quasi-periodic planar curves
• Attractors on an N-torus: Quasiperiodicity versus chaos
• Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
• Occurrence of strange Axiom A attractors near quasi periodic flows on \(T^m\), \(m\geq 3\)
• Fractal properties of critical invariant curves
• Frequency analysis for multi-dimensional systems. Global dynamics and diffusion
• Unfoldings of quasi-periodic tori in reversible systems
• Ergodic averages with deterministic weights
• Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems
• On the numerical computation of Diophantine rotation numbers of analytic circle maps
• From chaos to quasi-periodicity
• Numerical computation of the normal behaviour of invariant curves ofn-dimensional maps
• Quasi-Periodic Frequency Analysis Using Averaging-Extrapolation Methods
• Lagrangian tori near resonances of near-integrable Hamiltonian systems
• A KAM theorem without action-angle variables for elliptic lower dimensional tori
• Resonance regions for families of torus maps
• The parameterization method for invariant manifolds I: Manifolds associated to non-resonant subspaces
• KAM theory without action-angle variables
• Boundaries of Siegel disks: Numerical studies of their dynamics and regularity
• The Many Facets of Chaos
• A Parameterization Method for the Computation of Invariant Tori and Their Whiskers in Quasi‐Periodic Maps: Explorations and Mechanisms for the Breakdown of Hyperbolicity
• Small denominators. I. Mappings of the circumference onto itself
• Transitive homeomorphisms of the circle
• Continuation of Quasi-periodic Invariant Tori
• Unfoldings and bifurcations of quasi-periodic tori

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