Computer assisted proof for normally hyperbolic invariant manifolds

DOI10.1088/0951-7715/25/7/1997zbMath1256.37020arXiv1105.1277OpenAlexW2086789904MaRDI QIDQ2903935

Carles Simó, Maciej J. Capiński

Publication date: 2 August 2012

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.1277

zbMATH Keywords

attractornormally hyperbolic invariant manifolda posteriori verificationinterval-based numerical analysis

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Simulation of dynamical systems (37M05) Invariant manifold theory for dynamical systems (37D10) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (16)

Computing stable hierarchies of fiber bundles ⋮ Computing (un)stable manifolds with validated error bounds: non-resonant and resonant spectra ⋮ Rigorous enclosures of rotation numbers by interval methods ⋮ A parallel algorithm for the computation of invariant tori in large-scale dissipative systems ⋮ Rigorous computation of non-uniform patterns for the 2-dimensional Gray-Scott reaction-diffusion equation ⋮ Systematic Computer-Assisted Proof of Branches of Stable Elliptic Periodic Orbits and Surrounding Invariant Tori ⋮ Some questions looking for answers in dynamical systems ⋮ Distribution of stable islands within chaotic areas in the non-hyperbolic and hyperbolic regimes in the Hénon-Heiles system ⋮ Computation of maximal local (un)stable manifold patches by the parameterization method ⋮ Computer assisted error bounds for linear approximation of (un)stable manifolds and rigorous validation of higher dimensional transverse connecting orbits ⋮ Transition state theory with quasi-periodic forcing ⋮ Time dependent center manifold in PDEs ⋮ Polynomial approximation of one parameter families of (un)stable manifolds with rigorous computer assisted error bounds ⋮ Geometric proof for normally hyperbolic invariant manifolds ⋮ Detecting invariant manifolds as stationary Lagrangian coherent structures in autonomous dynamical systems ⋮ Existence of noise induced order, a computer aided proof

This page was built for publication: Computer assisted proof for normally hyperbolic invariant manifolds