Arc exchange systems and renormalization

Pinto, Alberto A.; Rand, David A.; Ferreira, Flávio

Publication

Arc exchange systems and renormalization

2010Journal article

dc.contributor.author	Pinto, Alberto A.
dc.contributor.author	Rand, David A.
dc.contributor.author	Ferreira, Flávio
dc.date.accessioned	2015-10-08T14:34:48Z
dc.date.available	2015-10-08T14:34:48Z
dc.date.issued	2010
dc.description.abstract	We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.	pt_PT
dc.identifier.citation	A.A. Pinto , D.A. Rand & F. Ferreira (2010) Arc exchange systems and renormalization, Journal of Difference Equations and Applications, 16:4, 347-371, DOI: 10.1080/10236190802422059	pt_PT
dc.identifier.doi	10.1080/10236190802422059
dc.identifier.issn	1023-6198
dc.identifier.uri	http://hdl.handle.net/10400.22/6657
dc.language.iso	eng	pt_PT
dc.peerreviewed	yes	pt_PT
dc.publisher	Taylor & Francis	pt_PT
dc.subject	Hyperbolic dynamics	pt_PT
dc.subject	Renormalization	pt_PT
dc.subject	Markov maps	pt_PT
dc.subject	Minimal sets	pt_PT
dc.title	Arc exchange systems and renormalization	pt_PT
dc.type	journal article
dspace.entity.type	Publication
oaire.citation.endPage	371	pt_PT
oaire.citation.issue	4	pt_PT
oaire.citation.startPage	347	pt_PT
oaire.citation.title	Journal of Difference Equations and Applications	pt_PT
oaire.citation.volume	16	pt_PT
person.familyName	Ferreira
person.givenName	Flávio
person.identifier.ciencia-id	9F13-D3C6-244B
person.identifier.orcid	0000-0001-7812-0983
person.identifier.rid	N-4562-2013
person.identifier.scopus-author-id	22978799800
rcaap.rights	openAccess	pt_PT
rcaap.type	article	pt_PT
relation.isAuthorOfPublication	6f67981a-3965-4ace-aec9-65938c4bcf66
relation.isAuthorOfPublication.latestForDiscovery	6f67981a-3965-4ace-aec9-65938c4bcf66