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SUMMARY:Appearance and Genericity of chaos
DTSTART:20130307T171500
DTEND:20130307T181500
DTSTAMP:20260610T151648Z
UID:39bc4ff1413032d49bfa9528249ac21f6267d2384d8558218c6ed146
CATEGORIES:Conferences - Seminars
DESCRIPTION:Yakov Pesin (Pennsylvania State University)\nI will discuss th
 e paradigm that is widely known as "deterministic chaos" -- the appearance
  of irregular chaotic motions in purely deterministic dynamical systems on
  compact phase spaces. This phenomenon is considered to be one of the most
  fundamental discoveries in the theory of dynamical systems in the second 
 part of the last century. It is due to instability of trajectories of the 
 system that drives orbits apart\, while compactness of the phase space for
 ces them back together. The consequent unending dispersal and return of ne
 arby trajectories is one of the hallmarks of chaos. The hyperbolic theory 
 of dynamical systems provides a mathematical foundation for that paradigm 
 and thus serves as a basis for the theory of chaos. The hyperbolic behavio
 r can be interpreted in various ways and the weakest one is associated wit
 h dynamical systems with non-zero Lyapunov exponents. I will introduce var
 ious types of hyperbolicity and will describe their appearance and generic
 ity. In particular\, I will discuss the still-open problem of whether dyna
 mical systems with non-zero Lyapunov exponents are generic. This genericit
 y problem is closely related to two other important problems in dynamics o
 n whether systems with non-zero Lyapunov exponents exist on any compact ph
 ase space and whether chaotic behavior can coexist with the regular one in
  a robust way.
LOCATION:CM 1 3 https://plan.epfl.ch/?room==CM%201%203
STATUS:CONFIRMED
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