Relativistic pendulum and invariant curves

Stefano Marò

doi:10.3934/dcds.2015.35.1139

Article Contents

2015, Volume 35, Issue 3: 1139-1162. Doi: 10.3934/dcds.2015.35.1139

This issue Previous Article Unified field equations coupling four forces and principle of interaction dynamics Next Article Robust transitivity of maps of the real line

Relativistic pendulum and invariant curves

Stefano Marò^1,

1.
Dipartimento di Matematica - Università di Torino, Via Carlo Alberto, 10, 10123 Torino

Received: December 31, 2013

Revised: July 31, 2014

Published: February 2015

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Abstract

We apply KAM theory to the equation of the forced relativistic pendulum to prove that all the solutions have bounded momentum. Subsequently, we detect the existence of quasiperiodic solutions in a generalized sense. This is achieved using a modified version of the Aubry-Mather theory for compositions of twist maps.

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Mathematics Subject Classification: Primary: 70H08, 70K43; Secondary: 34C15, 37C55.

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