Dynamical Systems and Ergodic Theory
Constructions
in Smooth Ergodic Theory
Given a collection of dynamical properties is it possible to find a
smooth map, possibly a diffeomorphism, of a compact manifold which
exhibits these properties. Ideally we seek obstructions to being able
to find any smooth model of a given collection of properties. For
actions of Z the only known obstruction is infinite entropy.
Dynamical
Cohomology
Additive cohomology classes determine the asymptotic behaviour of
Birkhoff sums and are crucial in studying diverse problems including
special flows and ergodic optimization. Mutiplicative cohomology
classes are crucial in various problems involving skew products and
special flows. Studying such equations over Anosov systems is the
content of Livšic Theory.
Non-Standard
Smooth Realizations of Liouville Rotations
B. Fayad, M. Saprykina, A. Windsor
(PDF 200K)
accepted to Ergodic Theory and Dynamical Systems
A Dichotomy Between Discrete and Continuous Spectrum for a Class of
Special Flows over Rotations
B. Fayad, A. Windsor
(PDF 220K)
accepted to the Journal of Modern Dynamics
Smoothness is not an Obstruction to Realizability
(PDF 148K)
accepted to Ergodic Theory and Dynamical Systems
A C
∞ Diffeomorphism with Infinitely Many Intermingled Basins.
I. Melbourne, A. Windsor
(PDF 152K)
accepted to Ergodic Theory and Dynamical Systems
Mixed Spectrum Reparametrizations of Linear Flows on T
2
B. Fayad, A. B. Katok, A. Windsor.
(PDF 244K)
Moscow Mathematical Journal, Vol. 1, Number 4, 2001
Minimal but not Uniquely Ergodic Diffeomorphisms.
(PDF 276K)
Proceedings of Symposia in Pure Mathematics: Smooth Ergodic Theory and
Its Applications
Amer. Math., Soc. Providence, RI, October 2001
An Approximated Solution to
Continuous-Time Stochastic Optimal Control Problems Through Markov
Decision Chains
by J. B. Krawczyk & A. Windsor
A Matlab Package for Approximating the Solution to a Continuous-
Time Stochastic Optimal Control Problem
by A. Windsor & J. B. Krawczyk
