|Speaker:||Professor Liang-Chung Hsia (National Central University)|
|Title:||On zeta functions associated to $p$-adic dynamics|
|Time:||2010-09-30 (Thu.) 15:00 - 16:00|
|Place:||Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)|
The study of $p$-adic dynamics has been very active in the past ten years as a branch of arithmetic dynamics. In the study of dynamical systems, the set of periodic points play an important role. Artin and Mazur introduced a one variable function, now called the dynamical zeta function, to enumerate periodic points of the dynamical systems in question. The dynamical zeta function provide important invariant about the dynamical systems.For $p$-adic dynamics, we consider the associated zeta functions of the dynamical systems over a non-archimedian field (in particular, a $p$-adic field). In particular, we will be mostly focusing on those dynamical systems whose zeta functions are rational functions. In the talk, we will discuss some related questions in $p$-adic dynamics and possibly some applications.
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