Bifurcation curves of subharmonic solutions

Gentile, G, Bartuccelli, MV and Deane, JHB (2006) Bifurcation curves of subharmonic solutions Reviews in Mathematical Physics 19 (2007), no. 3, 307-348.

	Text BDG-RMP-2007.pdf - ["content_typename_UNSPECIFIED" not defined] Restricted to Repository staff only Available under License : See the attached licence file. Download (593kB)
	Text (licence) SRI_deposit_agreement.pdf Restricted to Repository staff only Available under License : See the attached licence file. Download (33kB)

Abstract

We revisit a problem considered by Chow and Hale on the existence of subharmonic solutions for perturbed systems. In the analytic setting, under more general (weaker) conditions, we prove their results on the existence of bifurcation curves from the nonexistence to the existence of subharmonic solutions. In particular our results apply also when one has degeneracy to first order -- i.e. when the subharmonic Melnikov function vanishes identically. Moreover we can deal as well with the case in which degeneracy persists to arbitrarily high orders, in the sense that suitable generalisations to higher orders of the subharmonic Melnikov function are also identically zero. In general the bifurcation curves are not analytic, and even when they are smooth they can form cusps at the origin: we say in this case that the curves are degenerate as the corresponding tangent lines coincide. The technique we use is completely different from that of Chow and Hale, and it is essentially based on rigorous perturbation theory.

Item Type:	Article
Divisions :	Faculty of Engineering and Physical Sciences > Mathematics
Authors :	Gentile, G, Bartuccelli, MV and Deane, JHB
Date :	5 April 2006
DOI :	10.1142/S0129055X07002985
Related URLs :	Author Publisher
Depositing User :	Symplectic Elements
Date Deposited :	28 Mar 2017 10:50
Last Modified :	11 Jun 2019 08:44
URI:	http://epubs.surrey.ac.uk/id/eprint/806728

Actions (login required)

View Item

Downloads