This is an online research seminar on dynamical systems theory. It takes place every Friday (except Brazilian holidays) from 11 am to 12 am (local time in Rio de Janeiro, Brazil) using the platform zoom.

This seminar is part of an initiative to combat the current difficult situation of isolation and mathematical (not only) depression. In those times active resistance is fundamental. This is our proposal. We invite you to join us.

The seminar announcement is sent through the mailinglist DinamiCarioca (see also here).
If you are no member of "dinamicarioca" and are interested in receiving information about this seminar please send an email to rb.oir-cup.tam|0202acimanidaicnetsiser#rb.oir-cup.tam|0202acimanidaicnetsiser and you will be included in the mailing list of this seminar.


25 June | 10h30min | Special Session:

10:30-11:20| Jinhua Zhang (Beihang Univ., China)
Title: Centralizers of partially hyperbolic diffeomorphisms homotopic to Anosov automorphisms on T3

Abstract: In this talk, we will talk about the dynamics of partially hyperbolic diffeomorphisms homotopic to Anosov automorphisms on T3 and show that such diffeomorphism has virtually trivial centralizer or is smoothly conjuagte to its linear part. This is a joint work with S. Gan, Y. Shi and D. Xu.

11:30-12:20| Polina Vytnova (Univ. of Warwick, U.K.),
Title: Computing Hausdorff dimension of Bernoulli convolutions

Abstract: It is well known that for any 0<s<1 the sum of the infinite geometric series 1+s+s^2+ \ldots is 1/(1-s). Let us consider a similar expression where the signs are chosen at random, i.e. "+" and "-" in front of every term s^n are chosen with equal probability 1/2. The sum of the infinite series with randomly chosen signs is a random variable, and its law is a probability measure called the Bernoulli convolution.

It turns out the properties of this measure are very sensitive to the choice of s. For instance, if s<1/2, then it is supported on the Cantor set; if s = 1/2 then it is equal to the Lebesgue measure on [-2,2]. The case of s>1/2 is very intricate and has been a subject of intensive research which dates back to Erdos. To date, it is not known whether or not the measure is singular or absolutely continuous for a given s. The problem of computing the Hausdorff dimension of the measure is also open in general, though there have been several major advances in recent years.

In the talk I will discuss a new approach to uniform lower bounds on Hausdorff dimension of Bernoulli convolution measures which is based on random dynamics.

13:30-14:30| Pierre Berger (IMJ, Univ. Sorbonne, France),
Title: Renormalization nearby homoclinic tangencies, a formalism based on Banach algebras

Abstract: I will introduce a general techniques giving sharp bounds for renormalization nearby (chain of) homoclinic tangencies, and gives some applications to
the study of surface dynamics

More seminars in Upcoming seminars.

Organization: Lorenzo J. Díaz (PUC-Rio, Brazil)

Contact: rb.oir-cup.tam|0202acimanidaicnetsiser#rb.oir-cup.tam|0202acimanidaicnetsiser

Zoom access: PUC-Rio, Brazil.

ANNOUNCEMENT: the gmail-account moc.liamg|0202acimanidaicnetsiser#moc.liamg|0202acimanidaicnetsiser was blocked by some mysterious rule of Gmail that requires some security check. Provided cellphone numbers did not work (there appeared a mysterious message “This number was already used several times for confirmation.”, which was not true). We never forgot the password. We tried several cellphones.

In consequence, we also lost the access to the youtube account videos of previous seminars are deposited.

We also lost all contact addresses. We trying to recover most of them. In case you did not receive a message by September 1st, this will mean that we lost your contact and we apologize for that.