Computation of invariant tori by Newton-Krylov methods in large-scale dissipative systems

DOI10.1016/j.physd.2009.10.012zbMath1183.37137OpenAlexW1971183091MaRDI QIDQ2268944

Yanyan Li

Publication date: 15 March 2010

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2009.10.012

zbMATH Keywords

Newton-Krylov methodsresonancesvariational equationsinvariant toricontinuation methodsgeneralized Poincaré map

Mathematics Subject Classification ID

Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Bifurcations of singular points in dynamical systems (37G10) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Computational methods for bifurcation problems in dynamical systems (37M20)

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Uses Software

• ODEPACK
• Torcont

Cites Work

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• Newton-Krylov continuation of periodic orbits for Navier-Stokes flows
• Amplitude equations close to a triple-(+1) bifurcation point of \(\mathbb D_4\)-symmetric periodic orbits in \(\mathbb O(2)\)-equivariant systems
• On the reducibility of linear differential equations with quasiperiodic coefficients
• Computation, continuation, and bifurcation of torus solutions for dissipative maps and ordinary differential equations
• The Hopf-saddle-node bifurcation for fixed points of 3D-diffeomorphisms: The Arnol'd resonance web
• The quasi-periodic doubling cascade in the transition to weak turbulence
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• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
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• THE FOLD-FLIP BIFURCATION
• ON THE MULTIPLE SHOOTING CONTINUATION OF PERIODIC ORBITS BY NEWTON–KRYLOV METHODS
• SYMMETRIC PERIODIC ORBITS AND GLOBAL DYNAMICS OF TORI IN AN O(2) EQUIVARIANT SYSTEM: TWO-DIMENSIONAL THERMAL CONVECTION
• Continuation of Quasi-periodic Invariant Tori

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