Approximate renormalization for the break-up of invariant tori with three frequencies

Abstract

We construct an approximate renormalization transformation for Hamiltonian systems with three degrees of freedom in order to study the break-up of invariant tori with three incommensurate frequencies which belong to the cubic field $Q(\tau )$, where ${\tau }^3+{\tau }^2-2\tau -1=0$. This renormalization has two fixed points~: a stable one and a hyperbolic one with a codimension one stable manifold. We compute the associated critical exponents that characterize the universality class for the break-up of the invariant tori we consider.

5 pages, REVTeX

References in corpus (5)

• Kolmogorov-Arnold-Moser Renormalization-Group Approach to the Breakup of Invariant Tori in Hamiltonian Systems
• Universality for the breakup of invariant tori in Hamiltonian flows
• An approximate renormalization-group transformation for Hamiltonian systems with three degrees of freedom
• Critical Attractor and Universality in a Renormalization Scheme for Three Frequency Hamiltonian Systems
• A Version of Thirring's Approach to the KAM Theorem for Quadratic Hamiltonians with Degenerate Twist

Cited by in corpus (1)

• The Destruction of Tori in Volume-Preserving Maps