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«Talks: Monday F. Ledrappier  Entropy for compact manifolds: properties, regularity, rigidity Abstract: We consider the stochastic entropy for the ...»

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Our work is very much in the spirit of these developments. We dene yet another specicationlike property and construct examples to examine limitations of various approaches. The main result describes properties of the simplex of invariant measures under our specication-like assumption.

In particular, we show that the set of ergodic measures is dense in the simplex of all invariant measures and every invariant measure has a generic point. We need NOT to assume that our system has periodic points.

There are examples which allow to distinguish between our approach and old and more recent specication-like methods of Sigmund, Bowen, Climenhaga-Thompson, Pster-Sullivan.This talk is based on a joint work with Katrin Gelfert (UFRJ) and Martha Lacka (Jagiellonian University).

M. Benedicks  Whitney-Hölder continuity of the SRB measure for transversal families of smooth unimodal maps Abstract: We consider C 2 families t → ft of C 4 nondegenerate unimodal maps, restricted to the Collet-Eckmann parameters (the derivative at the critical value is growing exponentially) and prove upper and lower bounds for the weak dependence of the invariant measure as a function of t on this set of parameters. (Joint work with Viviane Baladi and Daniel Schnellman).

A. Fisher  Order-two Ergodic Theorems for Renewal Flows Abstract: Consider the set of points of increase of a Mittag-Leer process of parameter α ∈ (0, 1).

The magnication (geodesic) scenery ow of this fractal set is a Bernoulli ow of innite entropy. Via cocyles, we construct a natural innite ergodic measure for its translation (horocycle) scenery ow and prove an order-two ergodic theorem. We show via a renormalization argument that this result passes over to renewal processes of parameter α with regularly varying tails. The renormalization approximation is, more precisely, a log-average almost-sure invariance principle. (Joint with Marina Talet of Aix-Marseille University.) V. Climenhaga  Specication, hyperbolicity, and towers Abstract: Given a dynamical system with some hyperbolicity, the equilibrium states associated to suciently regular potentials often display stochastic behaviour. Two important tools for studying these equilibrium states are specication properties and tower constructions. I will describe how both uniform and non-uniform specication properties can be used to deduce existence of a tower with exponential tails, and hence to establish various statistical properties.

Participants

Albert M. Fisher, USP, São Paulo, Brazil............................... fisher.alby@gmail.com Alejandro Cabrera, UFRJ, Rio de Janeiro, Brazil...................... acabrera@labma.ufrj.br Alena Erchenko, Pennsylvania State University, USA........................... axe930@psu.edu Alessandra Bianchi, Universitá de Padova, Italy........................ bianchi@math.unipd.it AlexeyKorepanov, Warwick University, UK........................ a.korepanov@warwick.ac.uk Ali Golmakani, UFAL, Maceió, Brazil................................ aligolmakani@gmail.com Artem Raibekas, UFF, Niteroi, Brazil........................................... artem@impa.br Artur Oscar Lopes UFRGS, Porto Alegre, Brazil.................. arturoscar.lopes@gmail.com Carlos Vasquez, PUC, Valparaiso, Chile...................................cvasqueze@gmail.com Cesar Maldonado, Universidade de Chile, Chile..................... cmaldonado@dim.uchile.cl Daniel Reis de Oliveira, UFRJ, Rio de Janeiro, Brazil................ danielreis@im.ufrj.br Davi Obata, UFRJ, Rio de Janeiro, Brazil............................... davi.obata@gmail.com Dominik Kwietniak, Jagiellonian University, Poland............. dominik.kwietniak@uj.edu.pl Dominique Malicet, PUC, Rio de Janeiro, Brazil......................... mdominique@crans.org Edgardo Perez Reyes, USP, São Paulo, Brazil.......................... edgardomath@gmail.com Eduardo Garibaldi, UNICAMP, Campinas, Brazil................... garibaldi@ime.unicamp.br Elaís Cidely Souza Malheiro, IMPA, Rio de Janeiro, Brazil,............elaiscidely@gmail.com Enrique Pujals, IMPA, Rio de Janeiro, Brazil,..................................enrique@impa.br Feliks Przytycki, IMPAN, Poland............................................ feliksp@impan.pl François Ledrappier, University of Notre Dame, USA.......................... fledrapp@nd.edu Freddy Pablo Castro Vicente, UFRJ, Rio de Janeiro, Brazil.............jesbobar@hotmail.com Gastão Coelho Gomes, UFRJ, Rio de Janeiro, Brazil....................... gastao@im.ufrj.br Gerardo Barrera Vargas, IMPA, Rio de Janeiro, Brazil........................bvargas@impa.br Giorgio Turchetti, Universitá di Padova, Italy.................. giorgio.turchetti@bo.infn.it Hale Aytaç, UFBA, Salvador, Brazil.......................................aytachale@gmail.com Ian Melbourne, University of Warwick, UK........................ i.melbourne@warwick.ac.uk Isaia Nisoli, UFRJ, Rio de Janeiro, Brazil.................................... isaia@im.ufrj.br Javier Solano, UFF, Niteroi, Brazil........................................ osolano@id.uff.br Jennyer Smith Bohorquez Barrera, UFRJ...... jennyffer smith bohorquez@hotmail.com Jérôme Rousseau, UFBA, Salvador, Brazil........................... jerome.rousseau@ufba.br Jorge Delgado, UFF, Niteroi, Brazil.......................................jdelgado@mat.uff.br José Vieitez, Universidade de la Republica, Uruguay.................... jvieitez226@gmail.com Katrin Gelfert, UFRJ, Rio de Janeiro, Brazil............................... gelfert@im.ufrj.br Krerley Oliveira, UFAL, Maceió, Brazil......................................krerley@gmail.com Lucas Henrique Backes, IMPA, Brazil,........................................ lhbackes@impa.br Luciana Silva Salgado, UFBA, Salvador, Brazil....................... lusalgado.sol@gmail.com Luiz Felipe Nobili França, UFF, Niteroi, Brazil....................... felipe.nobili@gmail.com Manuel Stadlbauer, UFBA, Salvador, Brazil....................... manuel.stadlbauer@ufba.br Marco Lenci, Univiversitá di Bologna, Italy.............................. marco.lenci@unibo.it

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