Banca de DEFESA: MAURI CRISTIANO DA SILVA FARIA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : MAURI CRISTIANO DA SILVA FARIA
DATE: 22/07/2022
TIME: 15:00
LOCAL: meet.google.com/gpe-tkbp-ymm
TITLE:
KEY WORDS:

Physical measures. Transversality. Absolutely continuous measures. Partially hyperbolic attractors. Lyapunov exponents.

PAGES: 86
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

In this work, we prove the existence and nitude of physical measures supported in the partially hyperbolic attractor and whose central direction is neutral, satisfying a geometric transversality condition between the supported images on unstable directions. We also prove that these measures are absolutely continuous and the union of their basins has total volume in the basin of attraction of the attractor. Furthermore, we verify that if the attractor has neutral central direction and the action of the derivative on the unstable direction is close to conformal, then it is possible to perturb the dynamics in a way that satis es the geometric condition of transversality and, therefore, has nite absolutely continuous physical measures. At the end, we give some examples where these conditions are satis ed. In particular, we exhibit an example of a non-hyperbolic attractor, with negative central Lyapunov exponents (it is mostly contracting) and whose absolutely continuous physical measures and another example of an attractor that has positive and negative central Lyapunov exponents.

BANKING MEMBERS:
Externo à Instituição - PAULO CÉSAR RODRIGUES PINTO VARANDAS - UFBA
Externo à Instituição - NILS MARTIN ANDERSON - UFF
Externo à Instituição - DAVI LIMA DOS SANTOS - UFAL
Externo à Instituição - EBERSON FERREIRA DA SILVA - UFRPE
Interno - 2158926 - RICARDO TUROLLA BORTOLOTTI