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.


5 March | Reopening of the Dynamical Resistance

11h00 | Viviane Baladi (Sorbonne Université, France)
Title: A decade of progress on Sinai billiards using Ruelle transfer operators

Sinai billiards (or the periodic Lorentz gas) are natural dynamical systems which have been challenging mathematicians for half a century. In the past decade, a new tool to study them
has emerged : Ruelle transfer operators acting on scales of anisotropic Banach spaces. This tool was introduced in 2011 in the billiards setting by Mark Demers and Hong-Kun Zhang, who gave a
new proof of Lai-Sang Young's celebrated 1998 result of exponential mixing for the SRB measure of the billiard map.
I will survey the results obtained on dispersing billiards maps and flows using this approach, leading to recent work on the measure of maximal entropy (joint with Demers, 2020) and more general Gibbs states (joint with Demers, preprint).

12h10min | Natalia Jurga (Univ. of St Andrews,UK)
Title: Non-existence of the box dimension for dynamically invariant sets

Abstract: One of the key challenges in the dimension theory of smooth dynamical systems is in establishing whether or not the Hausdorff, lower and upper box dimensions coincide for invariant sets. For sets invariant under conformal dynamics, these three dimensions always coincide. On the other hand, considerable attention has been given to examples of sets invariant under non-conformal dynamics whose Hausdorff and box dimensions do not coincide. These constructions exploit the fact that the Hausdorff and box dimensions quantify size in fundamentally different ways, the former in terms of covers by sets of varying diameters and the latter in terms of covers by sets of fixed diameters. In this talk we introduce the first example of a dynamically invariant set with distinct lower and upper box dimensions. Heuristically, this describes that if size is quantified in terms of covers by sets of equal diameters, a dynamically invariant set can appear bigger when viewed at certain resolutions than at others.

14h00 | Amie Wikinson (Univ. Chicago, USA)
Title: The strong unstable foliation of an Anosov diffeomorphism

Abstract: I will discuss recent work with Avila and Crovisier (and related work with Eskin, Potrie and Zhang as well) on the following problem and some higher dimensional analogues: Let f be an Anosov diffeomorphism in dimension 3. Assume the unstable bundle is 2 dimensional and admits a dominated splitting into weak and strong unstable bundle. Under what hypotheses is the strong unstable foliation minimal?

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.