Lower and upper bounds for the splitting of separatrices of the pendulum under a fast quasiperiodic forcing

DOI10.1090/S1079-6762-97-00017-6zbMath0867.34035OpenAlexW1589150563MaRDI QIDQ4340893

Amadeu Delshams, Àngel Jorba, Vassili Gelfreich, Teresa M. Seara

Publication date: 15 June 1997

Published in: Electronic Research Announcements of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/228059

zbMATH Keywords

normal formsMelnikov functionFibonacci numbershomoclinic orbitssplitting of separatricesquasiperiodic forcingquasiperiodic perturbations

Mathematics Subject Classification ID

Normal forms for dynamical systems (37G05) Diophantine inequalities (11J25) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (1)

An expansion of the homoclinic splitting matrix for the rapidly, quasiperiodically, forced pendulum

Cites Work

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• The separation of motions in systems with rapidly rotating phase
• An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum
• Exponentially small splitting of separatrices under fast quasiperiodic forcing
• A rigorous implementation of the Jeans - Landau - Teller approximation for adiabatic invariants
• TWISTLESS KAM TORI, QUASI FLAT HOMOCLINIC INTERSECTIONS, AND OTHER CANCELLATIONS IN THE PERTURBATION SERIES OF CERTAIN COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS: A REVIEW

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