Separatrix chaos: new approach to the theoretical treatment

TL;DR

This paper introduces a novel theoretical approach to analyze separatrix chaos using a special separatrix map analysis, revealing larger-than-expected chaotic layer widths and explaining the facilitation of global chaos onset.

Contribution

The paper presents a new method for analyzing separatrix chaos, providing more accurate descriptions of chaotic layer boundaries and transport, and explains the facilitation of global chaos onset.

Findings

Chaotic layer width can be much larger than perturbation amplitude.

The approach accurately describes boundaries of the chaotic layer.

Simulations confirm the theoretical predictions.

Abstract

We develop a new approach to the theoretical treatment of the separatrix chaos, using a special analysis of the separatrix map. The approach allows us to describe boundaries of the separatrix chaotic layer in the Poincar\'{e} section and transport within the layer. We show that the maximum which the width of the layer in energy takes as the perturbation frequency varies is much larger than the perturbation amplitude, in contrast to predictions by earlier theories suggesting that the maximum width is of the order of the amplitude. The approach has also allowed us to develop the self-consistent theory of the earlier discovered (PRL 90, 174101 (2003)) drastic facilitation of the onset of global chaos between adjacent separatrices. Simulations agree with the theory.