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UID:7982@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20151103T110000
DTEND;TZID=Europe/Paris:20151103T120000
DTSTAMP:20241120T205619Z
URL:https://www.i2m.univ-amu.fr/evenements/some-relations-between-some-sta
 bility-notions/
SUMMARY:Dmitry Todorov (Centre de Recerca Matematica in Barcelona): Some re
 lations between some stability notions
DESCRIPTION:Dmitry Todorov: There is a strong and long-lasting interest in 
 chaotic dynamical systems as mathematical models of various processes in d
 ifferent areas of science.\nLike for any other mathematical models for cha
 otic systems to be useful it is desirable that they have stability propert
 ies.\nThere exist different stability properties\, “geometric” and “
 ergodic” ones. I am going to describe some of them in connection with my
  past and current research. The plan is to discuss the following notions a
 nd some relations between them\n• Uniform hyperbolicity (strong chaotici
 y based on coherent expansion and contraction in all points)\n• Structur
 al stability (stability of individual trajectories with respect to a small
  perturbation of a system as a whole)\n• (Inverse) shadowing (stability 
 of trajectories with respect to small per-iteration perturbations)\n• St
 ochastic stability (stability of statistical properties of a system with r
 espect to random per-iteration perturbations)\n• Twisted cohomological e
 quations and Weierstrass-like functions (special dynamics-related equation
 s and their solutions of a special kind having interesting properties)\n
 • Linear response (stability and good dependence of statistical properti
 es of a system with respect to a small perturbation of a system as a whole
 )\nI will try to be as short as possible in describing each one so that I 
 have time to cover most.\nhttps://arxiv.org/abs/1411.7604\n\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Dmitry_Todorov.jpg
CATEGORIES:Séminaire,Ernest
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