744 Motooka, Nishi-ku

Fukuoka 819-0395, Japan

TEL (Office): +81-92-802-4402

FAX (Office): +81-92-802-4405

##### IMI(Institute of Mathematics for Industry)

# Detail of Academic Staff

## TOYOKAWA, Hisayoshi/ Assistant Professor

TOYOKAWA, Hisayoshi（Assistant Professor） I study ergodic theory which deals with statistical properties of dynamical systems/random dynamical systems. Here, a (discrete time) dynamical system is a system described by some rule, such as a recursion formula, so that the next state after one unit time will be determined as soon as the current state is determined, and a random dynamical system is a perturbed dynamical system in some sense. Even if a system is complicated which is so called a chaotic dynamical system, under certain conditions including that it preserves some probability measure (which is called an invariant probability measure), several nice statistical properties as well as law of large numbers hold. On the other hand, abundant dynamical systems for which natural invariant measures are infinite measures have recently appeared (and hence we cannot hope law of large numbers) and have been vigorously studied, and I am interested in such phenomena occurred from infinite systems. In particular, I would like to research what kind of dynamical systems/random dynamical systems admit naturally infinite invariant measures and what kind of statistic properties hold for such systems.

Keyword | ergodic theory, dynamical system, random dynamical system |

Division | Fundamental Mathematics |