Computer assisted error bounds for linear approximation of (un)stable manifolds and rigorous validation of higher dimensional transverse connecting orbits

DOI10.1016/j.cnsns.2014.08.010zbMath1329.37081OpenAlexW2034752323MaRDI QIDQ907673

Jason D. Mireles James

Publication date: 26 January 2016

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2014.08.010

zbMATH Keywords

linear approximationstable and unstable manifoldscomputer assisted proof for connecting orbits in higher dimensionsvalidated computer assisted error bounds

Mathematics Subject Classification ID

Invariant manifold theory for dynamical systems (37D10) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Related Items (9)

A Framework for the Numerical Computation and A Posteriori Verification of Invariant Objects of Evolution Equations ⋮ Fourier-Taylor parameterization of unstable manifolds for parabolic partial differential equations: formalism, implementation and rigorous validation ⋮ Connecting Orbits for Compact Infinite Dimensional Maps: Computer Assisted Proofs of Existence ⋮ Validated numerics for equilibria of analytic vector fields: Invariant manifolds and connecting orbits ⋮ Parameterization method for unstable manifolds of delay differential equations ⋮ High-Order Parameterization of Stable/Unstable Manifolds for Long Periodic Orbits of Maps ⋮ Fourier-Taylor approximation of unstable manifolds for compact maps: numerical implementation and computer-assisted error bounds ⋮ Validated numerics for continuation and bifurcation of connecting orbits of maps ⋮ Analytic Continuation of Local (Un)Stable Manifolds with Rigorous Computer Assisted Error Bounds

Uses Software

• INTLAB
• CAPD
• Cosy

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