Document Type

Article

Publication Date

2013

Publication Title

Physica D

Volume

243

First Page

45

Last Page

63

DOI

10.1016/j.physd.2012.09.005

Abstract

Invariant tori play a fundamental role in the dynamics of symplectic and volume-preserving maps. Codimension-one tori are particularly important as they form barriers to transport. Such tori foliate the phase space of integrable, volume-preserving maps with one action and d angles. For the area-preserving case, Greene’s residue criterion is often used to predict the destruction of tori from the properties of nearby periodic orbits. Even though KAM theory applies to the three-dimensional case, the robustness of tori in such systems is still poorly understood. We study a three-dimensional, reversible, volume-preserving analogue of Chirikov’s standard map with one action and two angles. We investigate the preservation and destruction of tori under perturbation by computing the ‘‘residue’’ of nearby periodic orbits. We find tori with Diophantine rotation vectors in the ‘‘spiral mean’’ cubic algebraic field. The residue is used to generate the critical function of the map and find a candidate for the most robust torus.

Comments

This paper is a pre-print.

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