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(New page: = ACMS Abstracts: Fall 2013 = === Amit Einav (Cambridge) === TBA === Shilpa Khatri (UNC) === TBA)
 
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= ACMS Abstracts: Fall 2013 =
= ACMS Abstracts: Fall 2013 =
=== Rob Sturman (Leeds) ===
''Lecture 1: The ergodic hierarchy & uniform hyperbolicity''
Ergodic theory provides a hierarchy of behaviours of increasing
complexity, essentially covering dynamics from indecomposable,
through mixing, to apparently random. Demonstrating that a
(real) system possesses any of these properties is typically difficult,
but one important class of system - uniformly hyperbolic systems -
make the ergodic hierarchy immediately accessible. Uniform hyperbolicity
is a strong condition, and so we also describe its weaker counterpart,
non-uniform hyperbolicity. Our chief example in this lecture is the Arnold
Cat Map, an example of a hyperbolic toral automorphism.
''Lecture 2: Non-uniform hyperbolicity & Pesin theory''
The connection between non-uniform hyperbolicity and the ergodic
hierarchy is more difficult, but is made possible by the work of
Yakov Pesin in 1977, and extensions due to Katok & Strelcyn.
Here we illustrate the theory with a linked twist map, a paradigmatic
example of non-uniformly hyperbolic system.
''Rates of mixing in models of fluid flow''
The exponential complexity of chaotic advection might be reasonably
assumed to produce exponential rates of mixing. However, experiments
suggest that in practice, boundaries slow mixing rates down. We give
rigorous results from smooth ergodic theory which establishes polynomial
mixing rates for linked twist maps, a class of simple models of bounded flows.


=== Amit Einav (Cambridge) ===
=== Amit Einav (Cambridge) ===

Revision as of 15:13, 21 August 2013

ACMS Abstracts: Fall 2013

Rob Sturman (Leeds)

Lecture 1: The ergodic hierarchy & uniform hyperbolicity

Ergodic theory provides a hierarchy of behaviours of increasing complexity, essentially covering dynamics from indecomposable, through mixing, to apparently random. Demonstrating that a (real) system possesses any of these properties is typically difficult, but one important class of system - uniformly hyperbolic systems - make the ergodic hierarchy immediately accessible. Uniform hyperbolicity is a strong condition, and so we also describe its weaker counterpart, non-uniform hyperbolicity. Our chief example in this lecture is the Arnold Cat Map, an example of a hyperbolic toral automorphism.

Lecture 2: Non-uniform hyperbolicity & Pesin theory

The connection between non-uniform hyperbolicity and the ergodic hierarchy is more difficult, but is made possible by the work of Yakov Pesin in 1977, and extensions due to Katok & Strelcyn. Here we illustrate the theory with a linked twist map, a paradigmatic example of non-uniformly hyperbolic system.

Rates of mixing in models of fluid flow

The exponential complexity of chaotic advection might be reasonably assumed to produce exponential rates of mixing. However, experiments suggest that in practice, boundaries slow mixing rates down. We give rigorous results from smooth ergodic theory which establishes polynomial mixing rates for linked twist maps, a class of simple models of bounded flows.

Amit Einav (Cambridge)

TBA

Shilpa Khatri (UNC)

TBA