# Registered Data

## [02115] Theory and applications of random/non-autonomous dynamical systems Part III

**Session Date & Time**: 5B (Aug.25, 10:40-12:20)**Type**: Proposal of Minisymposium**Abstract**: Dynamical systems evolving in the existence of noise, is called random dynamical systems. The basic properties, such as stability, bifurcation, and statistical properties, of such random or non-autonomous dynamical systems have not been well studied in mathematics and physics. Recently, cooperative research on random dynamical systems has been developed in the fields in statistical and nonlinear physics, dynamical system theory, ergodic theory, and stochastic process theory. In this mini-symposium, we consider theory and applications of random dynamical systems. In Part III, we discuss infinite ergodicity and random dynamical systems.**Organizer(s)**: Hiroki Sumi, Yuzuru Sato, Kouji Yano, Takuma Akimoto**Classification**:__37H05__,__37A50__,__37A05__,__37H12__**Speakers Info**:- Jon Aaronson (Tel Aviv University)
- Kouji Yano (Osaka University)
- Toru Sera (Osaka University)
- Tomoki Inoue (Ehime University)

**Talks in Minisymposium**:**[04000] Generalized uniform laws for occupation times of intermittent maps****Author(s)**:**Toru Sera**(Osaka University)

**Abstract**: Interval maps with indifferent fixed points are called intermittent maps. In this talk, we impose the condition that the orbit stays away from indifferent fixed points at the final observation time. Under this condition, we study the scaling limit of occupation times. This talk is based on joint work with Jon. Aaronson (Tel Aviv).

**[04085] Estimates of invariant measures for random maps****Author(s)**:**Tomoki Inoue**(Ehime University)

**Abstract**: We consider a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. Especially, we consider random dynamical systems with indifferent fixed points and/or with unbounded derivatives. Under some conditions, such random dynamical systems have absolutely continuous invariant measures. We give some estimates of the absolutely continuous invariant measures.

**[04171] Arcsine and Darling--Kac laws for piecewise linear random interval maps****Author(s)**:**Kouji Yano**(Osaka University)

**Abstract**: We give examples of piecewise linear random interval maps satisfying arcsine and Darling--Kac laws, which are analogous to Thaler's arcsine and Aaronson's Darling--Kac laws for the Boole transformation. They are constructed by random switch of two piecewise linear maps with attracting or repelling fixed points, which behave as if they were indifferent fixed points of a deterministic map.

**[04503] probability and ergodic theory for inner functions****Author(s)**:**jon aaronson**(tel aviv university)- Kouji Yano (Osaka University)

**Abstract**: An analytic endomorphism of the unit disk is called an inner function if it's boundary limit defines a transformation of the circle - which is necessarily Lebesgue nonsingular. I'll review the ergodic theory of inner functions & present some results recently obtained with Mahendra Nadkarni.