Nonintegrability of nearly integrable dynamical systems near resonant periodic orbits

DOI10.1007/s00332-022-09802-zzbMath1497.37063arXiv2106.04930OpenAlexW3166039170MaRDI QIDQ2135635

Kazuyuki Yagasaki

Publication date: 9 May 2022

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.04930

zbMATH Keywords

perturbationresonancenonintegrabilityMelnikov methodMorales-Ramis theory

Mathematics Subject Classification ID

Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)

Related Items

Nonintegrability of forced nonlinear oscillators, Nonintegrability of dynamical systems near degenerate equilibria, Obstructions to integrability of nearly integrable dynamical systems near regular level sets

Cites Work

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• The Kuramoto model in complex networks
• Galoisian obstructions to non-Hamiltonian integrability
• A conceptual approach to the problem of action-angle variables
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Self-intersection of the complex separatrices and the nonexistence of the integrals in the Hamiltonian systems with one-and-half degrees of freedom
• Extended integrability and bi-Hamiltonian systems
• Galoisian obstructions to integrability of Hamiltonian systems. I.
• Nonintegrability of parametrically forced nonlinear oscillators
• Melnikov's method and codimension-two bifurcations in forced oscillations
• Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
• Degenerate resonances in forced oscillators
• Integrability and non-integrability in Hamiltonian mechanics
• Stable and Random Motions in Dynamical Systems
• Integrability of Hamiltonian systems and differential Galois groups of higher variational equations
• A nonlinear oscillator with a strange attractor
• Homoclinic motions and chaos in the quasiperiodically forced van der Pol-Duffing oscillator with single well potential
• A note on a connection between the Poincaré-Arnold-Melnikov integral and the Picard-Vessiot theory
• Persistence of periodic and homoclinic orbits, first integrals and commutative vector fields in dynamical systems
• The Melnikov Theory for Subharmonics and Their Bifurcations in Forced Oscillations
• Differential Galois theory and non-integrability of Hamiltonian systems