Chaos in the Kuramoto-Sivashinsky equations -- a computer-assisted proof.

DOI10.1016/S0022-0396(03)00104-9zbMath1050.37017OpenAlexW1981833819MaRDI QIDQ1414013

Daniel Wilczak

Publication date: 19 November 2003

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-0396(03)00104-9

zbMATH Keywords

covering relationsperiodic solutionKuramoto-Sivashinsky equationsymbolic dynamics

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Complex behavior and chaotic systems of ordinary differential equations (34C28) Symbolic dynamics (37B10) Numerical chaos (65P20) Approximation methods and numerical treatment of dynamical systems (37M99)

Related Items (11)

Heteroclinic connections between periodic orbits in planar restricted circular three body problem. II ⋮ On computer-assisted proving the existence of periodic and bounded orbits ⋮ Validated numerics for equilibria of analytic vector fields: Invariant manifolds and connecting orbits ⋮ A rigorous implicit \(C^1\) Chebyshev integrator for delay equations ⋮ Systematic Computer-Assisted Proof of Branches of Stable Elliptic Periodic Orbits and Surrounding Invariant Tori ⋮ Computer‐assisted analysis of chaos in a three‐species food chain model ⋮ Fourier-Taylor approximation of unstable manifolds for compact maps: numerical implementation and computer-assisted error bounds ⋮ Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems ⋮ Complexity in a Hybrid van der Pol System ⋮ CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems ⋮ Rigorous validation of a Hopf bifurcation in the Kuramoto-Sivashinsky PDE

Cites Work

• Unnamed Item
• Unnamed Item
• The existence of steady solutions of the Kuramoto-Sivashinsky equation
• Steady solutions of the Kuramoto-Sivashinsky equation
• Reversing \(k\)-symmetries in dynamical systems
• Heteroclinic connections in the Kuramoto-Sivashinsky equation: A computer assisted proof
• Fixed point index for iterations of maps, topological horseshoe and chaos
• Heteroclinic connections between periodic orbits in planar restricted circular three-body problem -- a computer-assisted proof
• \(C^1\) Lohner algorithm.
• Isolating neighborhoods and chaos
• Computer assisted proof of chaos in the Rössler equations and in the Hénon map
• Nonlinear analysis of hydrodynamic instability in laminar flames—II. Numerical experiments
• Set arithmetic and the enclosing problem in dynamics
• Symbolic dynamics for the Hénon-Heiles Hamiltonian on the critical level

This page was built for publication: Chaos in the Kuramoto-Sivashinsky equations -- a computer-assisted proof.