1
vote
2answers
365 views

$\{\phi:\int \phi d\mu=0\}$ for a fixed shift invariant $\mu$

Given a shift invariant probability measure $\mu$ on a mixing subshift of finite type. What are the Lipschitz functions with zero integral with respect to the measure $\mu?$ Clearly any ...
6
votes
2answers
400 views

Does the random Lorenz gas have a non-trivial diffusion coefficient?

For the periodic Lorenz gas Sinai showed that rescaling the trajectory of the tracer particle yields Brownian motion in the limit. Does there exist a similar result for the random Lorenz gas? If ...
8
votes
5answers
561 views

Persistence of fixed points under perturbation in dynamical systems

Suppose we have a smooth dynamical system on $R^n$ (defined by a system of ODEs). Assuming that the system has a finite set of fixed points, I am interested in knowing (or obtaining references about) ...
3
votes
0answers
180 views

What is known about first return times to Markov partitions for Anosov diffeomorphisms?

Consider an Anosov diffeomorphism $T: M \rightarrow M$ and a corresponding Markov partition $\mathcal{R}$ of $M$. For $x \in M$, let $\mathcal{R}(x)$ denote the element of $\mathcal{R}$ containing $x$ ...