Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
1993-10-22
Nonlinear Sciences
Adaptation and Self-Organizing Systems
39 pages postscript; use uudecode and uncompress ! 4 figures available as hardcopies on request
Scientific paper
10.1063/1.165952
In this paper we study parameter families of truncated horseshoes as models of multiscattering systems which show a transition to chaos without losing hyperbolicity, so that the topological features of the transition are completely describable by a parameterized family of symbolic dynamics. At a fixed parameter value the corresponding horseshoe represents the set of orbits trapped in the scattering region. The bifurcations are a pure boundary effect and no other bifurcations such as saddle center bifurcations occur in this transition scenario. Truncated horseshoes actually arise in concrete potential scattering under suitable conditions. It is shown that a simple scattering model introduced earlier can realize this scenario in a certain parameter range (the "truncated sawshoe") . For this purpose, we solve the inverse scattering problem of finding the central potential associated to the sawshoe model. Furthermore, we review classification schemes for the transition to chaos of truncated horseshoes originating from symbolic dynamics and formal language theory and apply them to the truncated double horseshoe and the truncated sawshoe.
No associations
LandOfFree
Truncated horseshoes and formal languages in chaotic scattering does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Truncated horseshoes and formal languages in chaotic scattering, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Truncated horseshoes and formal languages in chaotic scattering will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-398033