Chaotic maps, Hamiltonian flows and holographic methods

Thomas L. Curtright, Cosmas K. Zachos

Research output: Contribution to journalArticle

7 Scopus citations

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 quasi-Hamiltonian 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.

Original languageEnglish (US)
Article number445101
JournalJournal of Physics A: Mathematical and Theoretical
Volume43
Issue number44
DOIs
StatePublished - Nov 5 2010

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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