I will discuss the 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 forces them back together.
The consequent unending dispersal and return of nearby 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 behavior can be interpreted in various ways and
the weakest one is associated with dynamical systems with non-zero
I will introduce various types of hyperbolicity and will describe their
appearance and genericity. In particular, I will discuss the still-open
problem of whether dynamical systems with non-zero Lyapunov exponents
are generic. This genericity problem is closely related to two other
important problems in dynamics on whether systems with non-zero Lyapunov
exponents exist on any compact phase space and whether chaotic behavior
can coexist with the regular one in a robust way.
Dates of visit
Pennsylvania State University
07/03/2013 - 07/03/2013
Total Guests : 1
Dates of visit
Total Guests : 0
Conference in Honor of the 70th Birthday of Tudor Ratiu, 20 to 24 July 2020.
Registration fees of CHF 50.- are mandatory for visits from 1 day to full attendance of the conference.
Cancellations and no-shows are not eligible for a refund.
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