Chaotic maps, Hamiltonian flows and holographic methods
Abstract
Holographic functional methods are introduced as probes of discrete timestepped maps that lead to chaotic behavior. The methods provide continuous time interpolation between the time steps, thereby revealing the maps to be quasiHamiltonian systems underlain by novel potentials that govern the motion of a perceived point particle. Between turning points, the particle is strictly driven by Hamiltonian dynamics, but at each encounter with a turning point the potential changes abruptly, loosely analogous to the switchbacks on a mountain road. A sequence of successively deepening switchback potentials explains, in physical terms, the frequency cascade and trajectory folding that occur on the particular route to chaos revealed by the logistic map.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 November 2010
 DOI:
 10.1088/17518113/43/44/445101
 arXiv:
 arXiv:1002.0104
 Bibcode:
 2010JPhA...43R5101C
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 This paper, and its precedent arXiv:0909.2424 [mathph], are dedicated to Murray GellMann on the occasion of his 80th birthday