No Finite Invariant Density for Misiurewicz Exponential Maps
نویسنده
چکیده
For exponential mappings such that the orbit of the only singular value 0 is bounded, it is shown that no integrable density invariant under the dynamics exists on C.
منابع مشابه
Existence and Convergence Properties of Physical Measures for Certain Dynamical Systems with Holes
We study two classes of dynamical systems with holes: expanding maps of the interval and Misiurewicz maps. In both cases, we prove that there is a natural absolutely continuous conditionally invariant measure μ (a.c.c.i.m.) with the physical property that strictly positive Hölder continuous functions converge to the density of μ under the renormalized dynamics of the system. In addition, we con...
متن کاملTriviality of fibers for Misiurewicz parameters in the exponential family
We consider the family of holomorphic maps ez + c and show that fibers of postsingularly finite parameters are trivial. This can be considered as the first and simplest class of non-escaping parameters for which we can obtain results about triviality of fibers in the exponential family.
متن کاملErgodic properties of countable extensions
Roth, Samuel Joshua PhD, Purdue University, May 2015. Ergodic Properties of Countable Extensions. Major Professor: Micha l Misiurewicz. First, we study countably piecewise continuous, piecewise monotone interval maps. We establish a necessary and sufficient criterion for the existence of a non-decreasing semiconjugacy to an interval map of constant slope in terms of the existence of an eigenvec...
متن کاملRational Misiurewicz Maps Are Rare Ii
The notion of Misiurewicz maps has its origin from the paper [10] from 1981 by M. Misiurewicz. The (real) maps studied in this paper have, among other things, no sinks and the omega limit set ω(c) of every critical point c does not contain any critical point. In particular, in the quadratic family fa(x) = 1 − ax 2, where a ∈ (0, 2), a Misiurewicz map is a non-hyperbolic map where the critical p...
متن کاملRational Misiurewicz Maps for Which the Julia Set Is Not the Whole Sphere
We show that Misiurewicz maps for which the Julia set is not the whole sphere are Lebesgue density points of hyperbolic maps.
متن کامل