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Assume that $ (X,\mathcal{B},m,T) $ is a measure-preserving dynamical system, where $ (X,\mathcal{B},m) $ is a probability space, $ \mathcal{B} $ denotes all the measurable sets in $ X $, $ m $ is the ...

I am studying the paper Blumenthal - Statistical properties for compositions of standard maps with increasing coefficent. I have a problem to understand how the distortion estimates are used. The ...

This is related to discrete dynamical systems, with the initial condition $X_1$ being a random variable with a non singular distribution. The system is driven by the iteration $X_{n+1} = g(X_n)$ for ...

Let $(\mu_n)_{n=1}^{\infty}$ be a sequence in $\mathcal{P}_1(X)$ for some compact metric space $(X,d)$. Suppose that there is a weakly-continuous function $F:\mathcal{P}_1(X)\rightarrow \mathcal{P}_1(...

Start with $p_1$ a random point on the origin-centered unit circle $C$. At step $i$, select a random point $q_i$ on $C$, and a random mirror line $M_i$ through $q_i$, and reflect $p_i$ in $M_i$ to ...