The H non–Heiles Hamiltonian near the critical energy level—some rigorous results

DOI10.1088/0951-7715/16/5/316zbMath1040.37049OpenAlexW2025744565MaRDI QIDQ4466393

Piotr Zgliczyński, Gianni Arioli

Publication date: 9 June 2004

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/16/5/316

zbMATH Keywords

chaotic dynamicshomoclinic solutionsnumerical simulationsheteroclinic solutionselliptic periodic solutionssymmetric hyperbolic periodic solutions

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Periodic orbits of vector fields and flows (37C27) Symbolic dynamics (37B10) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory (37-04)

Related Items (6)

Validated numerics for equilibria of analytic vector fields: Invariant manifolds and connecting orbits ⋮ Using scattering theory to compute invariant manifolds and numerical results for the laser-driven Hénon-Heiles system ⋮ Computer assisted error bounds for linear approximation of (un)stable manifolds and rigorous validation of higher dimensional transverse connecting orbits ⋮ RIGOROUS VERIFICATION OF THE EXISTENCE OF TRANSVERSAL HOMOCLINIC ORBITS ⋮ Polynomial approximation of one parameter families of (un)stable manifolds with rigorous computer assisted error bounds ⋮ Numerical computation of orbits and rigorous verification of existence of snapback repellers

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