Variational method for locating invariant tori

Abstract

We formulate a variational fictitious-time flow which drives an initial guess torus to a torus invariant under given dynamics. The method is general and applies in principle to continuous time flows and discrete time maps in arbitrary dimension, and to both Hamiltonian and dissipative systems.

10 pages

References in corpus (4)

• Variational method for finding periodic orbits in a general flow
• Bailout Embeddings, Targeting of KAM Orbits, and the Control of Hamiltonian Chaos
• Relative Periodic Solutions of the Complex Ginzburg-Landau Equation
• Numerical Computation of the Stable and Unstable Manifolds of Invariant Tori

Cited by in corpus (7)

• Global structure of regular tori in a generic 4D symplectic map
• Quadratic Volume-Preserving Maps: Invariant Circles and Bifurcations
• Unstable manifolds of relative periodic orbits in the symmetry-reduced state space of the Kuramoto-Sivashinsky system
• Predicting chaotic statistics with unstable invariant tori
• Invariant tori in dissipative hyperchaos
• Canonical methods of constructing invariant tori by phase-space sampling
• Data-driven guessing and gluing of unstable periodic orbits