Highlights of chaos research
George Contopoulos
TL;DR
This paper reviews key developments in chaos theory, including the role of unstable periodic orbits, resonance overlap, Moser series, and quantum chaos, highlighting both classical and quantum aspects of chaotic systems.
Contribution
It summarizes recent advances in chaos theory, especially analytical formulas near unstable orbits and the quantum chaos framework via Bohmian mechanics.
Findings
Chaos occurs near unstable periodic orbits.
Large chaotic domains result from resonance overlap.
Recent developments include Moser series and quantum chaos insights.
Abstract
We describe some highlights in the theory of chaos, that started with Poincare (1899). Generic systems have both ordered and chaotic domains. Chaos appears mainly near un- stable periodic orbits. Large chaotic domains are due to resonance overlap. Two recent developments of the theory of chaos, refer (a) to the analytical formulae (Moser series) in the chaotic domains near unstable periodic orbits, and (b) quantum chaos, described by the Bohmian theory of orbits.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Protein Structure and Dynamics · Nonlinear Dynamics and Pattern Formation