Dimension of the universal attractor describing the periodically driven Sine-Gordon equations

DOI10.1080/00411458708204663zbMath0637.58017OpenAlexW2008391591MaRDI QIDQ3777108

Jean-Michel Ghidaglia, Roger M. Temam

Publication date: 1987

Published in: Transport Theory and Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00411458708204663

zbMATH Keywords

fractal dimensiondamped sine-Gordon equationuniversal attractor

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Second-order nonlinear hyperbolic equations (35L70) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Partial differential equations of mathematical physics and other areas of application (35Q99)

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Cites Work

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• Influence of solitons in the initial state on chaos in the driven damped sine-Gordon system
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Attractors of partial differential evolution equations and estimates of their dimension
• Global lyapunov exponents, kaplan-yorke formulas and the dimension of the attractors for 2D navier-stokes equations
• Determining modes and fractal dimension of turbulent flows
• Stability Theory for the Damped Sine-Gordon Equation