Oscillatory escape in a Duffing equation with a polynomial potential

DOI10.1006/jdeq.1997.3305zbMath0894.34033OpenAlexW2002787322MaRDI QIDQ1377538

Jiangong You, Mark Levi

Publication date: 16 February 1998

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/e9e836ba7e4399a2055a5dfaed7a320ed287761f

zbMATH Keywords

unbounded solutionHamiltonian dynamicsdiscontinuityquasiperiodic solutionKAM curves

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear ordinary differential equations and systems (34A34) Growth and boundedness of solutions to ordinary differential equations (34C11) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (11)

On the application of KAM theory to discontinuous dynamical systems ⋮ A piecewise smooth Fermi–Ulam pingpong with potential ⋮ Rareness of escaping orbits of the quasi-periodic Duffing equations with polynomial potentials ⋮ Complex dynamics in one-dimensional nonlinear Schrödinger equations with stepwise potential ⋮ Unboundedness in a Duffing equation with polynomial potentials ⋮ Lagrange stability for Duffing-type equations ⋮ The coexistence of quasi-periodic and blow-up solutions in a class of Hamiltonian systems ⋮ The coexistence of quasi-periodic and blow-up solutions in a superlinear Duffing equation ⋮ Diffusion speed in piecewise smooth billiards ⋮ Longtime closeness estimates for bounded and unbounded solutions of non-recurrent Duffing equations with polynomial potentials ⋮ Periodic and unbounded motions in asymmetric oscillators at resonance

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Quasiperiodic motions in superquadratic time-periodic potentials
• Boundedness of solutions for polynomial potentials with \(C^2\) time dependent coefficients
• Breakdown of stability of motion in superquadratic potentials
• Stable and Random Motions in Dynamical Systems
• Invariant curves and time-dependent potentials
• An unbounded solution of a superlinear Duffing's equation
• Boundedness for solutions of nonlinear periodic differential equations via Moser's twist theorem
• A case of boundedness in Littlewood's problem on oscillatory differential equations
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
• Unbounded Solutions of an Equation ÿ+g{y) =p(t) , with p(t) Periodic and Bounded, and g(y) /y → ∞ as y →±∞

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