Omri Sarig
I study the stochastic behavior of deterministic dynamical systems. Most of
my research deals with dynamical
systems which are not uniformly hyperbolic (or their symbolic dynamical
models) or systems which are defined on non-compact spaces. Rather than
seeking
to generalize the classical theory to such situations, I am looking for new
types of phenomena which do not
occur in the compact, or uniformly hyperbolic case.
In some cases, there is a large zoo of examples, and then my aim is to find
the most general theoretical results
possible which explain and classify the possible phenomena. My earliest
work, on the thermodynamic formalism
for topological Markov shifts with infinite alphabets, is of this type. In
other cases, I have the feeling that there
is a lack of examples showing what happens, and then I look for examples
rather than theories. My recent work
on horocycle flows on hyperbolic surfaces of infinite genus has this flavor.
Recent Publications
- Critical exponents for dynamical systems. Commun. Math. Phys. 267 (2006) 631-667.
- [with V. Cyr] Spectral gap and transience for Ruelle operators on countable Markov shifts. Communications in Mathematical Physics 292 (2009) 637-666.
- The horocycle flow and the Laplacian on hyperbolic surfaces of infinite genus. To appear in GAFA.