University of Surrey

Test tubes in the lab Research in the ATI Dance Research

Quasiperiodic attractors, Borel summability and the Bryuno condition for strongly dissipative systems

Gentile, G, Bartuccelli, MV and Deane, JHB (2006) Quasiperiodic attractors, Borel summability and the Bryuno condition for strongly dissipative systems JOURNAL OF MATHEMATICAL PHYSICS, 47 (7). ? - ?. ISSN 0022-2488

[img]
Preview
PDF
fulltext.pdf

Download (124Kb)

Abstract

We consider a class of ordinary differential equations describing one-dimensional analytic systems with a quasiperiodic forcing term and in the presence of damping. In the limit of large damping, under some generic nondegeneracy condition on the force, there are quasiperiodic solutions which have the same frequency vector as the forcing term. We prove that such solutions are Borel summable at the origin when the frequency vector is either any one-dimensional number or a two-dimensional vector such that the ratio of its components is an irrational number of constant type. In the first case the proof given simplifies that provided in a previous work of ours. We also show that in any dimension d, for the existence of a quasiperiodic solution with the same frequency vector as the forcing term, the standard Diophantine condition can be weakened into the Bryuno condition. In all cases, under a suitable positivity condition, the quasiperiodic solution is proved to describe a local attractor.

Item Type: Article
Uncontrolled Keywords: Science & Technology, Physical Sciences, Physics, Mathematical, Physics
Related URLs:
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:09
Last Modified: 23 Sep 2013 18:28
URI: http://epubs.surrey.ac.uk/id/eprint/461

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year


Information about this web site

© The University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom.
+44 (0)1483 300800