3 problems

Let $\mu_\eps$ be the invariant measure of a noisy dynamical system and let $\mu_{\mathrm{SRB}}$ be the corresponding SRB measure of the deterministic system. In uniformly hyperbol…

Limiting-measure conjecture. All limiting measures will be supported either at a stable equilibrium or on a stable periodic orbit.

Let $X$ be the constructed heteroclinic network, and let $\zeta>0$ denote the noise amplitude. Consider typical trajectories of the corresponding noisy system and the equilibria an…