Fractal structures in the Hénon-Heiles Hamiltonian

¹  GME, Universidad de Zaragoza - E-50009 Zaragoza, Spain, EU
²  Departamento Matemática Aplicada and IUMA, Universidad de Zaragoza - E-50009 Zaragoza, Spain, EU
³  Departamento Física Aplicada, Universidad de Zaragoza - E-50009 Zaragoza, Spain, EU

Corresponding author: rbarrio@unizar.es

Received: 8 November 2007
Accepted: 12 February 2008

Abstract

During the past few years, several papers (Aguirre J., Vallejo J. C. and Sanjuán M. A. F., Phys. Rev. E, 64 (2001) 066208; de Moura A. P. S. and Letelier P. S., Phys. Lett. A, 256 (1999) 362; Seoane J. M., Sanjuán M. A. F. and Lai Y.-C., Phys. Rev. E, 76 (2007) 061208) have detected the presence of fractal escape basins in Hénon-Heiles potentials in the unbounded range. Upon fixing the energy value, these basins are detected on the and planes. In this paper, we explore the appearance of different kinds of fractal structures. We present an analysis of the fractal structures on the escape basins of the and planes (allowing the energy value E to change and studying the fat-fractal exponent); later, we present these structures on the KAM tori for low energy values, on small regular islands inside the chaotic sea close to the critical energy level on the -plane, and most interestingly, on small regular regions inside the escape region. These small regions of bounded motion and regular behavior appear after the critical escape energy, when most of the orbits are escape orbits.