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Let $f$ be a $\mathcal{C}^1$ vector field on a compact subset $M \subset \mathbb{R}^n$. We define a dynamical system by $$\dot{x}(t)=f(x(t))$$ In ergodic theory, the occupation measure is $$\mu_{x, T}(...

Let $M$ be a differentiable manifold and $F \in \mathcal{X}(M)$. We define a DS by $$\dot{x}=F(x(t))$$ An ordered collection $\mathcal{M}=\left\{M_{1}, \ldots, M_{l}\right\}$ of compact subsets of ...