Banca de DEFESA: FABÍOLA DE OLIVEIRA PEDREIRA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE : FABÍOLA DE OLIVEIRA PEDREIRA
DATA : 02/07/2020
HORA: 09:00
LOCAL: Ambiente Virtual
TÍTULO:

ON THE BEHAVIOUR OF THE SINGULAR VALUES OF EXPANDING LORENZ MAPS

PALAVRAS-CHAVES:

Keywords: Expanding Lorenz, Lyapunov exponent, slow recurrence, two-parameter family, Hausdorff dimension

PÁGINAS: 98
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Matemática
RESUMO:

In this work we study one-dimensional expanding Lorenz maps f with the same singular point c. We show that if the orbits of singular values satisfy a condition of slow recurrence, then every ergodic invariant probability has slow recurrence to the singularity and it has finite Lyapunov exponent. Moreover, we show that generically the singular values do not belong to the basin of its SRB measure. Also, we show that singularity allows the existence of many ergodic invariant measures with full support, having positive entropy, fast recurrence to the singular region and infinite Lyapunov exponent. Furthermore, we consider a two-parameter standard family of these maps and prove that there is a cone in the parameter space, in which we find sets of points on the curves, which has positive Hausdorff dimension, so that the maps associated to these points have finite Lyapunov exponent for every ergodic invariant probability, and there is one and only one equilibrium state for a given H¨older potential.
Keywords: Expanding Lorenz, Lyapunov exponent, slow recurrence, two-parameter
family, Hausdorff dimension.

MEMBROS DA BANCA:
Interno - 1654597 - PAULO CESAR RODRIGUES PINTO VARANDAS
Interno - 1283019 - VILTON JEOVAN VIANA PINHEIRO
Externo à Instituição - ALBERTO ADREGO PINTO - UNIPORTO
Externo à Instituição - MANUEL STADLBAUER
Externo à Instituição - MARIA JOSÉ PACÍFICO