Rigidity of partially hyperbolic dynamical systems and Anosov systems
Geometry and topology under positive/nonnegative sectional curvature
| Grant number: | 13/16226-8 |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| Start date: | December 01, 2013 |
| End date: | January 31, 2017 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
| Principal Investigator: | Ali Tahzibi |
| Grantee: | Pablo Daniel Carrasco Correa |
| Host Institution: | Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil |
| Associated scholarship(s): | 14/11962-0 - Rigidity and foliations in dynamical systems, BE.EP.PD |
Abstract The proposed project consists of studying the rigidity properties of foliations, specially of those arising as invariant foliations for dynamical systems or general group actions.Our particular interest is understanding two types of results. 1) On the one hand, continue the study initiated by Prof. Ali Tahzibi and collaborators regarding the property of uniformly bounded density for foliations. This property, still not completely understood, seems to imply strong differentiability results for invariant foliations, a popular research topic in dynamical systems. 2) On the other hand, study the possibility of extending the rigidity results for abelian actions obtained recently by B. Kalinin, A. Katok e F. Rodriguez-Hertz to actions of abelian pseudo-groups, and in particular, to foliations with abelian holonomy. The fact of extending results of group theory to pseudo-groups is a usual technique in foliation theory, and being the referred rigidity results completely new, this possibility has not been pursued yet. (AU) | |
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