Nesta sexta-feira (03/07) teremos mais um encontro do Seminário de Sistemas Dinâmicos da UFF.
Desta vez, a palestra será conduzida por Yingjian Liu (IMPA), às 14h, na sala 409 do Bloco H, Gragoatá.
O título e resumo da palestra encontram-se abaixo:
Title: Regularity of Lyapunov Exponents at One-Point Spectra
Abstract:
We study the regularity of Lyapunov exponents for random matrix products
at probability measures exhibiting a one-point spectrum, that is, when
there is only one Lyapunov exponent. While continuity and Hölder
continuity of Lyapunov exponents are well understood under
irreducibility and simplicity assumptions, the degenerate case of a
collapsed spectrum is typically excluded due to the lack of hyperbolicity.
In this talk, we show that despite this degeneracy, the Lyapunov
exponents enjoys some regularity at one-point spectrum measures. Under
compactness and semisimplicity conditions, we prove pointwise
logarithmic Hölder continuity of the Lyapunov exponents with respect to
perturbations of the underlying probability measure. The mechanism
relies on a quantitative control of the random walk on projective space
and a careful analysis of mass accumulation governed by invariant structure.
Esperamos vocês!