Measures with Separable Orbits

Measures with Separable Orbits

Distorted Probabilities and m-Separable Fuzzy Measures

Distorted probabilities are an important family of fuzzy measures. In a recent paper we introduced m-dimensional distorted probabilities, which generalize the former and permit us to have a smooth transition from distorted probabilities to unconstrained ones. In this paper we introduce the union condition and the strict union condition, and we show that when these conditions hold for a fuzzy me...

On Separable Supports of Borel Measures

Some properties of Borel measures with separable supports are considered. In particular, it is proved that any σ-finite Borel measure on a Suslin line has a separable supports and from this fact it is deduced, using the continuum hypothesis, that any Suslin line contains a Luzin subspace with the cardinality of the continuum. Let E be a topological space. We say that the space E has the propert...

On Hyperbolic Measures and Periodic Orbits

We prove that if a diffeomorphism on a compact manifold preserves a nonatomic hyperbolic Borel probability measure, then there exists a hyperbolic periodic point such that the closure of its unstable manifold has positive measure. Moreover, the support of the measure is contained in the closure of all such hyperbolic periodic points. We also show that if an ergodic hyperbolic probability measur...

Pseudo-orbits, stationary measures and metastability

We study random perturbations of multidimensional piecewise expanding maps. We characterize absolutely continuous stationary measures (acsm) of randomly perturbed dynamical systems in terms of pseudo-orbits linking the ergodic components of absolutely continuous invariant measures (acim) of the unperturbed system. We focus on those components, called least-elements, which attract pseudoorbits. ...