Boundedness of solutions for a class of impact oscillators with time-dependent polynomial potentials

DOI10.3934/CPAA.2014.13.645zbMath1311.34070arXiv1301.6448OpenAlexW1970864778MaRDI QIDQ380157

Xiang Sun, Da-Xiong Piao

Publication date: 13 November 2013

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.6448

zbMATH Keywords

canonical transformationboundedness of solutionsimpactor oscillatorsMoser's small twist theoremtime-dependent polynomial potentials

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Growth and boundedness of solutions to ordinary differential equations (34C11)

Cites Work

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• Existence of quasi-periodic solutions and Littlewood's boundedness problem of sub-linear impact oscillators
• Existence of quasiperiodic solutions and Littlewood's boundedness problem of super-linear impact oscillators
• Boundedness for the general semilinear Duffing equations via the twist theorem
• Invariant tori for asymptotically linear impact oscillators
• Quasiperiodic motions in superquadratic time-periodic potentials
• Invariant tori of Duffing-type equations
• Boundedness in nonlinear oscillations at resonance
• Chaotic, regular and unbounded behaviour in the elastic impact oscillator
• Periodic orbits of a collinear restricted three-body problem
• Non-smooth dynamical systems
• Invariant tori in Hamiltonian systems with impacts
• Dual billiards, twist maps and impact oscillators
• Invariant curves and time-dependent potentials
• Boundedness in a Piecewise Linear Oscillator and a Variant of the Small Twist Theorem
• Large amplitude periodic bouncing for impact oscillators with damping
• Bouncing solutions of an equation with attractive singularity
• Periodic Motions of Linear Impact Oscillators via the Successor Map

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