Non-integrability of Hamiltonian systems through high order variational equations: summary of results and examples

DOI10.1134/S1560354709030010zbMath1229.37058MaRDI QIDQ653230

Carles Simó, Regina Martínez

Publication date: 9 January 2012

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

zbMATH Keywords

spring-pendulum systemdifferential Galois theorynon-integrability criteriahigher order variationals

Mathematics Subject Classification ID

Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics (70H07) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)

Related Items (10)

Some questions looking for answers in dynamical systems ⋮ Liouville integrability: an effective Morales-Ramis-Simó theorem ⋮ Numerical integration of high-order variational equations of ODEs ⋮ Linearised higher variational equations ⋮ Measuring the total amount of chaos in some Hamiltonian systems ⋮ Picard-Vessiot theory and integrability ⋮ Swinging Atwood Machine: experimental and numerical results, and a theoretical study ⋮ On the stability of periodic Mercury-type rotations ⋮ Conditions and evidence for non-integrability in the Friedmann-Robertson-Walker Hamiltonian ⋮ Third order integrability conditions for homogeneous potentials of degree −1

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