RSCRM

Smooth Ergodic Theory and Partially Hyperbolic Diffeomorphisms

Coordinatore	Consorci Centre de Recerca Matematica    more  Organization address address: FACULTAD CIENCIES UAB APRATADO 50 city: BELLATERRA postcode: 8193 contact info Titolo: Mr. Nome: Oriol Cognome: Fernández Leyva Email: send email Telefono: -935811047 Fax: -935812168
Nazionalità Coordinatore	Spain [ES]
Totale costo	0 €
EC contributo	145˙937 €
Programma	FP7-PEOPLE Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	FP7-PEOPLE-IEF-2008
Funding Scheme	MC-IEF
Anno di inizio	2009
Periodo (anno-mese-giorno)	2009-09-01   -   2011-08-31

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	Consorci Centre de Recerca Matematica  Organization address address: FACULTAD CIENCIES UAB APRATADO 50 city: BELLATERRA postcode: 8193 contact info Titolo: Mr. Nome: Oriol Cognome: Fernández Leyva Email: send email Telefono: -935811047 Fax: -935812168	ES (BELLATERRA)	coordinator	145˙937.11

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 Obiettivo del progetto (Objective)

'The project deals with the interplay between some local and global aspects of discrete dynamical systems. In the first part we consider several problems related to the Entropy Conjecture. For any map f on a compact manifold M there are some invariants measuring the dynamical complexity at the ‘global’ level (homological or homotopical), like the spectral radius of the map induced on homology, the fundamental-group entropy, etc. In some situations these global invariants give a lower bound for some other ‘local’ invariants, which are in general harder to compute, like the topological entropy or the volume growth. We are interested in studying the relationship between the global and local invariants for different classes of maps, in particular the relationship between the volume growth and the invariants related to the fundamental group of M. On the second part of the proposal we consider partially hyperbolic diffeomorphisms (PHDs). One can associate to the stable and unstable foliations some closed currents or transversal measures, and consequently homology classes. In some situations one can relate the action induced by f on these homology classes with the volume growth of disks inside the leaves of the foliations, and consequently with the topological entropy of the map. For Anosov systems this was done by Shub-Williams and Ruelle-Sullivan, and for PHDs this was done in some cases by Saghin-Xia. We want to investigate when one can establish such relationships, and what are the possible applications of them.'