arXiv subjects
Publications and source records attributed to Ali Sarizadeh.
By benefit of Pesin's method to prove ergodicity with respect to Lebesgue measure for ordinary dynamical systems, we conclude ergodicity (resp. term-ergodicity) for some action semigroups with respect to volume measure (resp. quasi measure). To this aim, the main tool is the theory of local ergodicity.
We prove that every expanding minimal semigroup action of $C^1$ diffeomorphisms of a compact manifold (resp. $C^{1+α}$ conformal) is robustly minimal (resp. ergodic with respect to Lebesgue measure). We also show how, locally, a blending region yields the robustness of the minimality and implies ergodicity.
We study the minimality of almost every orbital branch of minimal iterated function systems (IFSs). We prove that this kind of minimality holds for forward and backward minimal IFSs generated by orientation-preserving homeomorphisms of the circle. We provide new examples of iterated functions systems where this behavior persists under perturbation of the generators.
In this work, we introduce the concept of term ergodicity for action semigroups and construct semigroups on two dimensional manifolds which are $C^{1+α}$-robustly term ergodic. Moreover, we illustrate the term ergodicity by some exciting examples. At last, we study a problem in the context of circle packing which is concerned to term ergodic.