Thematic Program on

Dynamical Systems
School of Mathematics, IPM,
February - May, 2017

 School of Mathematics

 Home Calendar Conference Participants Photos Practical Information

 Workshop and Conference in Dynamical Systems School of Mathematics, IPM May 20-23, 2017
Schedule:

 9:30 - 10:45 10:45 - 11:15 11:15 - 12:30 12:30 - 14:00 14:00 - 15:30 15:30 - 16:00 16:00 - 17:10 Saturday Durand mini-course (1) Tea Kocsard Lunch Talebi (Photo) Tea Talk 1 Sunday Durand mini-course (2) Tea Talks 2 & 3 Lunch Talk 4 Tea Monday Durand mini-course (3) Tea Talk 5 Lunch Fakhari Tea Tuesday Durand mini-course (4) Tea Hosseini Lunch Eslami Tea Durand

Registration:
 The attendance is free, but requires registration. Please fill out the registration form and send it to gt@ipm.ir with the subject  WCDS. Deadline: Wednesday, May 17, 2015 (بیست‌وهفتم اردیبهشت)

Location:
 Lecture Hall 1, Niavaran Building, IPM

Mini-Course:

 Fabien Durand (Univ. Picardie, France) Cobham’s theorem and substitution subshifts (4 lectures) This lecture intends to propose a first contact with subshift dynamical systems through the study of a well known family: the substitution subshifts. This will include a short introduction to topological dynamical systems and combinatorics on words. We will focus on the unique ergodicity of substitution subshifts and we will obtain, as a corollary, a proof of a seminal result on automata theory: the Cobham's theorem. (More info)

Invited Talks (70 min.):

 Fabien Durand (Univ. Picardie, France) Automorphism groups of low complexity subshifts     [Slides] In this talk we discuss the structure of the automorphism groups of subshifts with respect to their complexities. We concentrate on subshift with zero entropy. Peyman Eslami (Warwick Univ.) Exponential memory loss for piecewise expanding maps of metric spaces I will briefly discuss work in progress on studying the exponential memory loss for piecewise expanding $C^{1+}$ maps with countably many branches on metric spaces. I will mostly discuss the sufficient conditions for proving such a result including the conditions on the complexity growth of the partition elements. We will not assume or use the existence of a Markov structure for such dynamical systems and give explicit estimates on the constants involved in the exponential decay. Abbas Fakhari (Shahid Beheshti Univ.) Balanced and unbalanced product of  $\rm{SL}(2,\mathbb{R})$  elements In this talk we discuss about the product of SL(2,R) elements in generic and non generic fashions. Providing an equivalent condition for the uniform hyperbolicity of cocycles over a full shift of finite type, we try to recognize its complement. We also state some relevant results on unbalanced products. Maryam Hosseini (IPM) Cocycles and continuous spectrum of cantor minimal systems   Existence of cohomological equations for continuous spectrum of Cantor minimal systems was firstly investigated by Orme in 1995. Modifying the result of Orme, we will show how continuous eigenvalues are related to the set of values of the invariant measures on the state space. Using that we compare "different" dynamical systems in an orbit equivalence class of Cantor minimal systems in terms of recurrence and mixings. The talk is based on the joint work with Thierry Giordano and David Handelman. Alejandro Kocsard (UFF, Brazil) On the dynamics of periodic point free homeomorphisms of  $\mathbb{T}^2$ By a result due to M. Handel, we know that the rotation set of a periodic point free homeomorphism of the $2$-torus which is isotopic to the identity has empty-interior. So, one can study directional rotational deviations for such dynamical systems. In this talk we shall discuss some recent results relating the existence of some invariant topological structures, called pseudo-foliations, with the boundedness of directional rotational deviations for such a system. Then we will show how this invariant pseudo-foliations can be used to get some dynamical information of the system and we shall discuss some new "a priori boundedness" results for minimal homeomorphisms whose rotation set is not just a point. Amin Talebi (Sharif U.T. & Paris 13) Non statistical dynamics on two dimensional manifolds Far from the world of hyperbolic dynamics, there are systems showing more complicated behaviors. For instance, it can happen that for a non-hyperbolic map on a manifold, the distribution of the orbit of Leb.a.e point in the phase space could not be "described" by an invariant measure. We investigate the existence of maps showing this particular behavior, in an explicit family of rational maps on Riemann sphere.

Expository Talks (40 min.):

 Expositor: Title / Reference of lecture: Hessam Rajabzadeh (IPM) Talk 1 On simultaneous linearization of diffeomorphisms of the sphere by D. Dolgopyat and R. Krikorian Maliheh Dabbaghian (Univ. Guilan) Talk 2 Large sets of integers and hierarchy of mixing properties of measure-preserving systems by V. Bergelson and Downarowicz Mohammad Reza Bagherzad Talk 3 Quadratic maps without asymptotic measure by Hofbauer and Keller Ali Barzanouni (Hakim Sabzevari Univ.) Talk 4 Szemeredi’s Theorem via Ergodic Theory by Y. Zhao Mehrdad Anvari (Sharif U.T.) Talk 5 Multiple mixing from weak hyperbolicity by the Hopf argument by Coudène, Hasselblatt, Troubetzkoy

 Organizer: Meysam Nassiri (IPM)

 School of Mathematics, IPM - Institute for Research in Fundamental Sciences Niavaran Building, Niavaran Square, Tehran, Iran Tel: +98 21 222 90 928 Email: gt@ipm.ir