Induced expansion for quadratic polynomials
Infinite invariant measures for non-uniformely expanding transformations of [0, 1]: weak law of large numbers with anamalous scaling.
Informal remarks on the orbit structure of discrete approximations to chaotic maps.
Intrinsic Ergodicity of Affine Maps in [0, 1]d.
Invariant densities for C¹ maps
We consider the set of expanding maps of the circle which have a unique absolutely continuous invariant probability measure whose density is unbounded, and show that this set is dense in the space of expanding maps with the topology. This is in contrast with results for or maps, where the invariant densities can be shown to be continuous.
Invariant Measures and Minimal Sets of Horospherical Flows.
Invariant measures and the compactness of the domain
We consider piecewise monotonic and expanding transformations τ of a real interval (not necessarily bounded) into itself with countable number of points of discontinuity of τ’ and with some conditions on the variation which need not be a bounded function (although it is bounded on any compact interval). We prove that such transformations have absolutely continuous invariant measures. This result generalizes all previous “bounded variation” existence theorems.
Invariant measures exist under a summability condition for unimodal maps.
Invariant Measures of C...-Diffeomorphisms of Markov Type in R...
Invariant measures of the geodesic flow and measures at infinity on negatively curved manifolds
Invariant sets with zero measure and full Hausdorff dimension.
Isomorphism of regular Morse dynamical systems