A Computer-Assisted Proof of $\Sigma_3$-Chaos in the Forced Damped Pendulum Equation

DOI10.1137/070695599zbMath1160.70010OpenAlexW2042865597MaRDI QIDQ3624471

László Hatvani, Tibor Csendes, Balázs Bánhelyi, Barnabas M. Garay

Publication date: 30 April 2009

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/070695599

zbMATH Keywords

interval arithmeticBrouwer's fixed point theoremtransition graph

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Computational methods for problems pertaining to mechanics of particles and systems (70-08) Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Interval and finite arithmetic (65G30)

Related Items (9)

On computer-assisted proving the existence of periodic and bounded orbits ⋮ An optimization technique for verified location of trajectories with prescribed geometrical behaviour in the chaotic forced damped pendulum ⋮ Optimal circle covering problems and their applications ⋮ Stability problems for the mathematical pendulum ⋮ Chaotic dynamics in a vertically driven planar pendulum ⋮ Nonintegrability of forced nonlinear oscillators ⋮ Chaos in Vallis' asymmetric Lorenz model for \textit{El Niño} ⋮ Reduction Methods and Chaos for Quadratic Systems of Differential Equations ⋮ On the existence and stabilization of an upper unstable limit cycle of the damped forced pendulum

Uses Software

• C-XSC 2.0
• PROFIL/BIAS
• GAIO

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