The twist coefficient of periodic solutions of a time-dependent Newton's equation

DOI10.1007/BF01048263zbMath0761.34036WikidataQ115394566 ScholiaQ115394566MaRDI QIDQ1199841

Rafael Ortega

Publication date: 17 January 1993

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

zbMATH Keywords

\(T\)-periodic solutionexamplesLyapunov stabletwist typependulum of variable length

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Stability of solutions to ordinary differential equations (34D20)

Related Items (17)

Stable odd solutions of some periodic equations modeling satellite motion. ⋮ Twist periodic solutions of repulsive singular equations ⋮ Lyapunov stability of periodic solutions of the quadratic Newtonian equation ⋮ Quantifying Poincaré's continuation method for nonlinear oscillators ⋮ Twist periodic solutions in the relativistic driven harmonic oscillator ⋮ The linearization of periodic Hamiltonian systems with one degree of freedom under the Diophantine condition ⋮ Periodic solutions for a class of non-autonomous Newton differential equations ⋮ Stability and bifurcations of even periodic orbits in the Sitnikov problem ⋮ The Lyapunov stability for the linear and nonlinear damped oscillator with time-periodic parameters ⋮ Lyapunov stability of elliptic periodic solutions of nonlinear damped equations ⋮ Boundedness in asymmetric oscillations under the non-resonant case ⋮ Radial stability of periodic orbits of damped Keplerian-like systems ⋮ Optimal conditions for maximum and antimaximum principles of the periodic solution problem ⋮ The stability of the equilibrium of a nonlinear planar system and application to the relativistic oscillator ⋮ On the motion of an oscillator with a periodically time-varying mass ⋮ Twist character of the fourth order resonant periodic solution ⋮ The method of lower and upper solutions and the stability of periodic oscillations

Cites Work

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• Subharmonic solutions for second order differential equations
• On the inversion of some differentiable mappings with singularities between Banach spaces
• Stability of a periodic problem of Ambrosetti-Prodi type
• Generic bifurcations of the twist coefficient
• A Multiplicity Result for Periodic Solutions of Forced Nonlinear Second order Ordinary Differential Equations
• Periodic Orbits and Solenoids in Generic Hamiltonian Dynamical Systems
• Computation of the Stability Condition for the Hopf Bifurcation of Diffeomorphisms on $\mathbb{R}^2 $

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