Historic behavior and pluripotent property for diffeomorphisms
Shin Kiriki (Tokai Univ., Japão)

In “history,” statistical methods are completely ineffective in describing changes in individual events. Thus, it was Ruelle who called it historic if there is a behavior for which the average (one of the most fundamental concepts in statistics) could not be defined. I will introduce the fact that there are persistent non-hyperbolic dynamical systems that exhibit historic behavior, which is an affirmative answer to Takens’ last problem. Moreover, the property that a dynamical system can be statistically approximated not only by historic behaviors but also by any other behaviors is called pluripotent. If time permits, I would also like to introduce the robust existence of pluripotent dynamical systems in the nonhyperbolic class. This talk is an introduction not only to [Kiriki-Soma’17] and [Kiriki-Nakano-Soma’23], but also to the ongoing collaboration with Professor Lorenzo J. Diaz.