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SUMMARY:Series of Talks
DTSTART;VALUE=DATE-TIME:20260721T130000Z
DTEND;VALUE=DATE-TIME:20260721T150000Z
DTSTAMP;VALUE=DATE-TIME:20260807T032218Z
UID:indico-event-11482@ictp.it
DESCRIPTION:\n	15:00 - 15:30 Marks Ruziboev\, National Pedagogical Univer
 sity of Uzbekistan \n\n	 \n\n	On the Dynamics of Mean-Field Coupled Inter
 val Maps with Singularities\n\n	\n		 \n	\n		Abstract: In this talk\, we p
 resent some results for mean-field coupled interval maps with finitely man
 y singularities in the thermodynamic limit. Therefore\,  the dynamics is
  governed by a nonlinear\, self-consistent transfer operator.  We show t
 hat when the individual maps have good spectral properties\, the coupled s
 ystem also admits a unique equilibrium\, which is exponentially stable. 
 \n		 \n\n\n	 \n\n	15:40 -16:10 Alejandro Passeggi\, Universidad de la 
 República\, Uruguay\n\n	 \n\n	Topological Criteria for Annular Chaos \n
 \n	\n		 \n	\n		Abstract: Although paradigmatic models of chaotic dynamics
  in low-dimensional systems are well understood\, proving that a given sys
 tem exhibits chaotic behavior often remains a challenging task. Moreover\,
  identifying the underlying mechanisms responsible for such dynamics is fr
 equently beyond the scope of the classical literature on the subject.\n	\n
 		In recent years\, several topological criteria have been established for
  systems whose Poincaré map is defined on the annulus. These criteria pro
 vide simple and robust conditions guaranteeing the existence of chaos in t
 he form of a rotational horseshoe. Roughly speaking\, it is enough to find
  two topological disks with different rotation behavior under one iteratio
 n and whose forward iterates visit each other. This approach yields rigoro
 us proofs of chaotic dynamics while relying on elementary information abou
 t the system [1\,2]. Furthermore\, effective implementations of these crit
 eria have led to several concrete applications [3\,4].\n	\n		In this talk\
 , I will review these results and discuss recent progress toward a natural
  next step: obtaining explicit constructions of the rotational horseshoe o
 nce the above criteria (or related ones) have been verified. Such construc
 tions not only yield a rigorous computation of the map’s topological ent
 ropy\, but also allow one to locate the rotational horseshoe and its assoc
 iated essential instability region.\n	\n		 \n	\n		[1] A. Passeggi and F. 
 A. Tal\, Conditions Implying Annular Chaos\, accepted to Inventiones Mathe
 maticae.\n	\n		[2] A. Passeggi and F. Pirán\, Annular Chaos for Non-Wande
 ring Homeomorphisms\, arXiv.\n	\n		[3] M. J. Capiński\, M. Gröger\, A. P
 asseggi and F. A. Tal\, Conditions Implying Annular Chaos: Qualitative Res
 ults and CAP\, arXiv.\n	\n		[4] M. J. Capiński\, S. Llavayol and A. Passe
 ggi\, Rotational Chaos in the Driven Pendulum (to appear).\n		 \n\n\n	 \
 n\n	16:30 -17:00 Ali Tahzibi\, Universidade de São Paulo\, Brazil\n\n	 
 \n\n	Stably exponentially mixing endomorphisms\n	\n		 \n	\n		In a joint w
 ork with M. Hedyehloo\, M. Nassiri\, and H. Rajabzadeh\, we obtain new exa
 mples of stable exponentially mixing endomorphisms beyond the uniformly ex
 panding setting.\n	\n		More precisely\, we obtain two distinct C1 open cla
 sses of maps:\n	\n		1. A set U of endomorphisms that are neither uniformly
  expanding nor admitting any dominated splitting\, yet every smooth map in
  U has an ACIP and is exponentially mixing\,\n	\n		2. Another set V of end
 omorphisms that are not uniformly hyperbolic but do admit dominated splitt
 ing\, and every smooth map in V has an ACIP and is exponentially mixing.\n
 	\n		These sets are in the isotopy class of arbitrary uniformly expanding 
 maps. The results are in the framework of virtually expanding endomorphism
 s introduced by M. Tsujii.\n		 \n\n\n\n//indico.ictp.it/event/11482/
LOCATION:
URL://indico.ictp.it/event/11482/
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