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Title: Rotation number of integrable symplectic mappings of the plane

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.

Authors:
 [1];  [1];  [2]
  1. Fermilab
  2. Oak Ridge
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1418136
Report Number(s):
FERMILAB-PUB-17-305-AD-APC-CD
1649868
DOE Contract Number:  
AC02-07CH11359
Resource Type:
Journal Article
Resource Relation:
Journal Name: TBD
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Arnold-Liouville theorem; KAM theory; discrete dynamical systems; integrability; McMillan map; symplectic topology; Poincare rotation number

Citation Formats

Zolkin, Timofey, Nagaitsev, Sergei, and Danilov, Viatcheslav. Rotation number of integrable symplectic mappings of the plane. United States: N. p., 2017. Web.
Zolkin, Timofey, Nagaitsev, Sergei, & Danilov, Viatcheslav. Rotation number of integrable symplectic mappings of the plane. United States.
Zolkin, Timofey, Nagaitsev, Sergei, and Danilov, Viatcheslav. Tue . "Rotation number of integrable symplectic mappings of the plane". United States. doi:. https://www.osti.gov/servlets/purl/1418136.
@article{osti_1418136,
title = {Rotation number of integrable symplectic mappings of the plane},
author = {Zolkin, Timofey and Nagaitsev, Sergei and Danilov, Viatcheslav},
abstractNote = {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.},
doi = {},
journal = {TBD},
number = ,
volume = ,
place = {United States},
year = {Tue Apr 11 00:00:00 EDT 2017},
month = {Tue Apr 11 00:00:00 EDT 2017}
}