Symplectic analysis of dynamical systems with a small parameter. A new criterion for stabilization of homoclinic separatrices and its application

DOI10.1007/BF01062626zbMath0786.58016OpenAlexW1976216265MaRDI QIDQ1189757

I. O. Antonishin, Yu. O. Mitropol's'kii, Anatoliy K. Prykarpatsky, Valeriy H. Samoylenko

Publication date: 27 September 1992

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01062626

zbMATH Keywords

stabilizationbifurcationsymplectic manifoldshyperbolic singular pointhomoclinic separatrix

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Stability theory for smooth dynamical systems (37C75)

Cites Work

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• A criterion for non-integrability of Hamiltonian systems with nonhomogeneous potentials
• Non-integrability of Hénon-Heiles system and a theorem of Ziglin
• Existence of exponentially unstable periodic solutions and the non- integrability of homogeneous Hamiltonian systems
• An example of bifurcation to homoclinic orbits
• Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom
• Bifurcation to divergence and flutter in flow-induced oscillations: An infinite dimensional analysis
• A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam
• Stable and Random Motions in Dynamical Systems
• Deformation of Hamiltonian dynamics and constants of motion in dissipative systems
• Hamiltonian perturbation theory and water waves
• Homoclinic Orbits in Slowly Varying Oscillators
• The Mel’nikov Technique for Highly Dissipative Systems
• Averaging and Chaotic Motions in Forced Oscillations
• Melnikov’s method and Arnold diffusion for perturbations of integrable Hamiltonian systems
• Necessary condition for the existence of algebraic first integrals