Chaotic maps, Hamiltonian flows and holographic methods

Thomas Curtright, Cosmas K. Zachos

Research output: Contribution to journalArticle

7 Citations (Scopus)

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

Fingerprint

Hamiltonians
Chaotic Map
Turning Point
Hamiltonian Dynamics
Logistic map
Chaotic Behavior
Folding
Hamiltonian Systems
Cascade
Continuous Time
Chaos
Probe
Strictly
Interpolate
logistics
Trajectory
roads
mountains
Chaos theory
encounters

ASJC Scopus subject areas

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

Cite this

Chaotic maps, Hamiltonian flows and holographic methods. / Curtright, Thomas; Zachos, Cosmas K.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 43, No. 44, 445101, 05.11.2010.

Research output: Contribution to journalArticle

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