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INdAM Fellowship Programs in Mathematics and/or Applications cofunded by Marie Skłodowska-Curie Actions



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Peyman Eslami

INdAM-COFUND Incoming fellow between 2012-06-04 and 2014-06-03

Project information

Title

Characterizing the stability of absolutely continuous invariant measures of piecewise expanding dynamical systems

Partner organisation

Università  degli Studi di Roma “Tor Vergata”

Via della Ricerca Scientifica, 1
00133 Roma, Italy

http://web.uniroma2.it/

Abstract

In the field of Dynamical Systems stability plays an important role in theory and applications.

We will study the stability of absolutely continuous invariant measures (ACIMs) of dynamical systems with respect to various perturbations near periodic turning points. This study aims to characterize the stability of ACIMs of dynamical systems starting from piecewise expanding maps of the interval and to expand the results to more general systems.

In our approach we shall establish a connection between the stability of a dynamical system and the escape rates of conditionally invariant measures in certain associated open dynamical systems. Our main goal is to develop precise criteria for the stability of ACIMs of dynamical systems.

Fellow information

Previous positions, awards

  • Jan-Jun 2012: Research Assistant Professor, Concordia
    University
  • Sep 2010-Jan 2011: CMR/FQRNT International Internship
    Fellowship held at Indiana University Purdue University
    Indianapolis
  • September 2008: Carolyn and Richard Renaud Teaching
    Assistantship Award, Concordia University
  • 2001-2005: Fast-Track Scholarship, University of Alabama
    at Birmingham

Publications, preprints, other works

  1. P. Eslami, P. Góra, Stronger Lasota-Yorke inequality for one-dimensional piecewise expanding transformations, to appear in Proc. Amer. Math. Soc.
  2. Zh. Li, P. Góra, A. Boyarsky, H. Proppe, P. Eslami, A Family of Piecewise Expanding Maps having Singular Measure as a limit of ACIMs, to appear in Ergodic Theory Dynam. Systems.
  3. P. Góra, A. Boyarsky, P. Eslami, Metastable systems as random maps, to appear in the Internat. J. Bifur. Chaos Appl. Sci. Engrg.
  4. P. Eslami, M. Misiurewicz, Singular limits of absolutely continuous invariant measures for families of transitive maps, J. Difference Equ. Appl. 18 (2012) 739-750.
  5. P. Eslami, P. Góra, On eventually expanding maps of the interval, Amer. Math. Monthly 118 (2011) 629-635.
  6. G. Acosta, P. Eslami, L. G. Oversteegen, On open maps between dendrites, Houston J. Math. 3 (2007) 753-770.

Conferences, schools, other events

  • On the acim-stability of piecewise expanding dynamical systems
    Talk delivered at at Banff International Research Station
    Banff, Alberta, Canada, 2012
  • Singular limits of absolutely continuous invariant measures
    Talk delivered at at IUPUI Dynamical Systems Seminar
    Indianapolis, Indiana, USA, 2010
  • On eventually expanding maps of the unit interval
    Talk delivered at Talk delivered at Institut des Sciences Mathéatique
    Montréal, Québec, Canada, 2009
  • The dynamics of homeomorphism on dendrites
    Talk delivered at Talk delivered at the Spring Topology and Dynamical Systems Conference
    Birmingham, Alabama, USA, 2004
  • ICTP-ESF School and Conference in Dynamical Systems
    ICTP, Trieste, Italy, May 2012
  • Fields Institute Workshop on Recent Advances in
    Topological and Measure-Theoretic Methods in Dynamical Systems

    Nipissing University, North Bay, Ontario, Canada, May 2010
  • Summer School in Probability
    Pacific Institute for the Mathematical Sciences, Vancouver, British Columbia, Canada, June 2009
  • 40th Annual Iranian Mathematics conference
    Sharif University of Technology, Tehran, Iran, August 2008
  • Spring Topology and Dynamical Systems Conference
    The university of North Carolina Greensboro, Greensboro, North Carolina, USA, March 2006
  • Spring Topology and Dynamical Systems Conference
    Berry College, Rome, Georgia, USA, March 2005


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