Investigating non-integrability and chaos in complex time

DOI10.1016/0167-2789(95)00106-EzbMath0890.58023OpenAlexW2008835306MaRDI QIDQ1896541

Tassos C. Bountis

Publication date: 29 August 1995

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(95)00106-e

zbMATH Keywords

ordinary differential equationsnon-integrability

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Nonlinear ordinary differential equations and systems (34A34) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Ordinary differential equations of infinite order (34A35)

Related Items (8)

The splitting of separatrices, the branching of solutions, and nonintegrability of many-dimensional systems. application to the problem of the motion of a spherical pendulum with an oscillating suspension point ⋮ Galoisian obstruction to the integrability of general dynamical systems ⋮ Differential Galoisian approach to Jacobi integrability of general analytic dynamical systems and its application ⋮ Understanding complex dynamics by means of an associated Riemann surface ⋮ Non-integrability and chaos in classical cosmology. ⋮ Evidence of a natural boundary and nonintegrability of the mixmaster universe model ⋮ Relationship between singularities in classical mechanics for complex initial conditions and for complex time ⋮ Painlevé analysis and integrable cases of coupled cubic oscillators in the plane.

Cites Work

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• Integrability and non-integrability in Hamiltonian mechanics
• A direct approach to finding exact invariants for one-dimensional time-dependent classical Hamiltonians
• Singularity clustering in the Duffing oscillator
• Ratio-Like and Recurrence Relation Tests for Convergence of Series
• Non-integrable systems with algebraic singularities in complex time
• WHAT CAN COMPLEX TIME TELL US ABOUT REAL TIME DYNAMICS?
• On the non-integrability of a family of Duffing-van der Pol oscillators
• Necessary condition for the existence of algebraic first integrals

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