A Homoclinic Orbit in a Planar Singular ODE---A Computer Assisted Proof

DOI10.1137/120901271zbMath1284.34070OpenAlexW2076664574WikidataQ112207290 ScholiaQ112207290MaRDI QIDQ2871371

Piotr Zgliczyński, Robert Szczelina

Publication date: 22 January 2014

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/7d0b248e1d831c4ccfab9983d23075b9a5a7b1ee

zbMATH Keywords

invariant manifoldscone conditionshomoclinic connectionscomputer assisted proofscompacton traveling waves

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Algorithms with automatic result verification (65G20) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (11)

Recent advances in a rigorous computation of Poincaré maps ⋮ 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 ⋮ Continuation of homoclinic orbits in the suspension bridge equation: a computer-assisted proof ⋮ Rigorous numerics for fast-slow systems ⋮ Computation of maximal local (un)stable manifold patches by the parameterization method ⋮ Computing Evans functions numerically via boundary-value problems ⋮ Existence and stability of traveling pulse solutions of the FitzHugh-Nagumo equation ⋮ An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs ⋮ Connecting Orbits for a Singular Nonautonomous Real Ginzburg--Landau Type Equation ⋮ Stationary Coexistence of Hexagons and Rolls via Rigorous Computations

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