Rotation number of integrable symplectic mappings of the plane

2017/04/10 by Timofey Zolkin, Sergei Nagaitsev, Zolkin, Timofey +3 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1704.03077

openalex publication_date 2017/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Symplectic mappings are discrete-time analogs of Hamiltonian systems. They appear in many areas of physics, including, for example, accelerators, plasma, and fluids. Integrable mappings, a subclass of symplectic mappings, are equivalent to a Twist map, with a rotation number, constant along the phase trajectory. In this letter, we propose a succinct expression to determine the rotation number and present two examples. Similar to the period of the bounded motion in Hamiltonian systems, the rotation number is the most fundamental property of integrable maps and it provides a way to analyze the phase-space dynamics.

Cited by

• Geometry of Almost-Conserved Quantities in Symplectic Maps. Part III: Approximate Invariants in Nonlinear Accelerator Systems
• Geometry of Almost-Conserved Quantities in Symplectic Maps. Part I: Perturbation Theory
• Geometry of Almost-Conserved Quantities in Symplectic Maps. Part II: Recovery of approximate invariant

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