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
minicourse (1) 
Tea 
Kocsard

Lunch 
Talebi

(Photo) 
Tea 
Talk 1 

Sunday

Durand
minicourse (2) 
Tea 
Talks
2 & 3

Lunch 
Talk 4


Tea 


Monday

Durand
minicourse (3) 
Tea 
Talk 5

Lunch 
Fakhari


Tea 


Tuesday

Durand
minicourse (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

MiniCourse:
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 emptyinterior. 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 pseudofoliations, with
the boundedness of directional rotational
deviations for such a system. Then we will
show how this invariant pseudofoliations
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
nonhyperbolic 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
measurepreserving 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

