• Speakers

       김태형 (KIAS)

       오주미 (성균관대학교)

       이정훈 (전남대학교)

       정상태 (인하대학교)

       홍순기 (포스텍)

• 일정
  2월 11일 (화)
    14:00-15:00: 정상태
    15:00-15:30: Group Photo
    15:30-16:30: 오주미
    16:40-17:40: 이정훈
    19:00 -  :   Dinner
  2월 12일 (수)
    10:00-11:00: 홍순기
    11:30-12:30: 김태형
  
  

• 강연정보
  김태형(KIAS) 
  Title: Special divergent trajectories on the space of affine lattices.
  Abstract: In the theory of dynamical systems, the asymptotic behavior of typical trajectories has long been a central focus. Recently, however, there has been growing interest in studying divergent trajectories, particularly on homogeneous spaces such as the space of lattices. In this talk, we will explore special classes of divergent trajectories on the space of affine lattices and discuss their connections to Diophantine approximation.
  
  오주미(성균관대학교)
  Title: Dynamics Beyond Hyperbolic Structure : Spectral Decomposition for Homeomorphisms on Non-metrizable Spaces
  Abstract: The study of dynamical systems is motivated by the search of knowledge about the orbits behavior. Among the many type of orbit structures, hyperbolicity is the property that characterizes the stability of a given dynamical system.
  In this talk, we will discuss the stability of dynamical systems with respect to hyperbolicity and, in particular, stability results for dynamical systems with various expansive properties. Then we introduce the notions of symbolic expansivity and symbolic shadowing for homeomorphisms on non-metrizable compact spaces which are generalizations of expansivity and shadowing, respectively, for metric spaces. The main result is to generalize the Smale's spectral decomposition theorem to symbolically expansive homeomorphisms with symbolic shadowing on non-metrizable compact Hausdorff totally disconnected spaces. Furthermore, we consider the topological stability for homeomorphisms on that space.

이정훈(전남대학교)
Title: Structural stability of nonarchimedean chaotic dynamics
Abstract: In this talk, we mainly consider the chaotic locus of nonarchimedean dynamics, and its structural stabilities. More precisely, this talk will present three parts of structural stability for the nonarchimedean Julia set. In the first part, which is based on the author’s own work, we will see a nonarchimedean analogue of the celebrated result by Mañe-Sad-Sullivan in complex dynamics. These results implies hyperbolic dynamics is structurally stable so it is natural to ask if hyperbolic dynamics is only dynamics with structural stability, which can be regarded as a nonarchimedean analogues of Fatou conjecture in complex dynamics. We will obtain a negative answer of this nonarchimedean Fatou conjecture in our second part, which is based on the joint work with Prof. Robert Benedetto. Namely, it will turn out that it is possible to extend our structural stability theorem with much weaker assumptions than so-called hyperbolicity. In third part of our talk, we will give a different approach to this stability based on the joint work with Prof. Tomoki Kawahira. This will gives another reasoning of our weaker hyperboilicity found in the joint work with Prof. Robert Benedetto.

정상태(인하대학교)
Title: Metrical properties of beta-transformations on power series rings
Abstract: Let ${\mathbb{A}}_{\infty}$ be an integer ring of a formal Laurent series field in one variable $\frac{1}{t}$ over a finite field of order $q$, with a maximal ideal ${\mathbb{M}}_{\infty}.$ Then, we introduce beta-transformations $U_{\b}$ on   ${\mathbb{A}}_{\infty}$   that are topologically isomorphic and measurably isomorphic to the well-known beta-transformation $T_{\b}$ on ${\mathbb{M}}_{\infty}.$ We prove various metrical properties of $U_{\b}$ such as (total) ergodicity and mixing of any order through explicit representations of both $U_{\b}$ and its $n$th iterate $U_{\b}^n$ with respect to the shift operators. Furthermore, we examine dynamical connections between the measure-preserving property of 1-Lipschitz functions and the locally scaling property of $(q^{-k}, q^k)$-Lipschitz functions, in terms of the coefficients of van der Put and Carlitz—Wagner.

홍순기(포스텍)
Title: Distribution of closed geodesics on surface related to odd continued fractions
Abstract: In this talk, we investigate the distribution of closed geodesics on the quotient space of $\mathbb{H}^2$ by a group $$\Gamma:=\left\{M\in \operatorname{PGL}_2(\mathbb{Z}):\begin{pmatrix}1 &0\\0&1\end{pmatrix},\begin{pmatrix}0&1\\1&1\end{pmatrix}\, or \, \begin{pmatrix}1 &1\\1&0\end{pmatrix}\,\text{(mod\, 2)}\right\}.$$
Using the relation between the set of closed geodesics in $\Gamma\backslash \mathbb{H}^2$ and the set of periodic odd continued fractions, we describe the distribution of closed geodesics. For this, we adapt a modified version of Pollicott's method. This talk includes a comparison of the methods used for regular continued fractions and odd continued fractions. This work is a joint work with Seul Bee Lee.

• Transportation (오시는길)
  
  

• 참가자 목록(가나다 순):  고계원, 권상훈, 김동한, 김태형, 손영환, 신보미, 오주미, 이건희, 이슬비, 이정훈, 정상태, 차병철, 한지영, 홍순기, Nguyen Thanh Nguyen
  
  

• Organizer: 손영환 (yhson@postech.ac.kr)

• 지원: NRF,  포스텍 수학과