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.


09 April | 11h00min | Pablo Carrasco (UFMG, Belo Horizonte, Brazil)
Title: Extended flexibility for Anosov and Expanding maps.

Abstract: An active topic of research nowadays is understanding the restrictions (or lack thereof, called flexibility) for the Lyapunov exponents in a given isotopy class. This has the roots in the work of J. Bochi, A. Katok and F. Rodriguez-Hertz, who proposed a program to analyze these questions and gave several answers for Anosov diffeomorphisms. However, their tools seem to have some limitations, and in particular have the restriction that the metric entropy do not increase in the isotopy class.
In the first part of the talk I will report on some recent work with Radu Saghin (PUCV) where we develop some global perturbations methods for conservative systems, and apply these to establish flexibility results in the Anosov setting, allowing the metric entropy to increase. In particular, it is possible to obtain conservative partially hyperbolic DAs that have larger metric entropy that its linear part.
In the final section I will explain some variations of these techniques for the endomorphism case and analyze the same questions in the isotopy class of an expanding map in the 2-torus; as an example, I will discuss the fact that one can find truly NUH systems in such a class. This last part is a joint project with R. Saghin and M. Andersson (UFF).

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.