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arXiv · 1002.0104

Chaotic Maps, Hamiltonian Flows, and Holographic Methods

Thomas L. Curtright·Cosmas K. Zachos
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Abstract

Holographic functional methods are introduced as probes of discrete time-stepped 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.

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Thomas L. Curtright, Cosmas K. Zachos. 2010-01-31. Chaotic Maps, Hamiltonian Flows, and Holographic Methods. https://doi.org/10.1088/1751-8113/43/44/445101

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