6533b870fe1ef96bd12d07f9

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Universality for the breakup of invariant tori in Hamiltonian flows

M. GovinHans-rudolf JauslinHans KochCristel Chandre

subject

Mathematical analysisFOS: Physical sciencesFixed pointNonlinear Sciences - Chaotic DynamicsBreakup01 natural sciences010305 fluids & plasmasUniversality (dynamical systems)Hamiltonian systemsymbols.namesakeQuadratic equationPhase space0103 physical sciencessymbolsChaotic Dynamics (nlin.CD)010306 general physicsHamiltonian (quantum mechanics)ScalingMathematical physicsMathematics

description

In this article, we describe a new renormalization-group scheme for analyzing the breakup of invariant tori for Hamiltonian systems with two degrees of freedom. The transformation, which acts on Hamiltonians that are quadratic in the action variables, combines a rescaling of phase space and a partial elimination of irrelevant (non-resonant) frequencies. It is implemented numerically for the case applying to golden invariant tori. We find a nontrivial fixed point and compute the corresponding scaling and critical indices. If one compares flows to maps in the canonical way, our results are consistent with existing data on the breakup of golden invariant circles for area-preserving maps.

yearjournalcountryeditionlanguage
1998-06-01Physical Review E
https://doi.org/10.1103/physreve.57.6612