Loukas ZACHILAS

University of Thessalia
Department of Civil Engineering
Pedio Areos
38334 Volos
Greece
zachilas@rigas.uth.gr
 

Using color and rotation for visualizing 4D Poincare cross sections

Abstract: The problems encountered in the study of three-dimensional Hamiltonian systems by means of the Poincare cross-sections are reviewed. A new method to overcome these problems is proposed. In order to visualize the 4D "space" of section we introduce the use of color and rotation. We apply this method to the case of a family of simple periodic orbits in a three-dimensional potential and we describe the differences in the orbital behavior between regions close to stable and unstable periodic orbits.