2026年度 京都力学系セミナー
2026 Kyoto Dynamical Systems seminar
2026 Kyoto Dynamical Systems seminar
ハイブリッドで開催します (場合によってはオンラインまたは対面のみで行う可能性もあります)．
今後の予定
10月23日(金) Tamara Kucherenko氏 (The City College of New York), Philippe Thieullen氏（University of Bordeaux）
10月30日(金) 杉山登志氏（岐阜薬科大学）
11月27日(金) Rudolf Daniel Prokaj氏 (University of North Texas) (対面のみ，部屋6号館809室)
12月18日(金) 大野玄道氏（京都大学）
1月19日(火) 和田 康司 氏(北海道大学) [応用数学セミナーと共催] (対面のみ，部屋6号館809室，16:45開始)
講演のタイトルと概要（新しい順に並べてあります） Titles and Abstracts
11月27日(金) Rudolf Daniel Prokaj氏 (University of North Texas) (対面のみ，部屋6号館809室)
Box-like self-affine iterated function systems with rotations
Abstract:
We call a planar iterated function system box-like with rotations if the defining maps have diagonal or anti-diagonal linear parts with both types present. Up to a linear change of coordinates, IFSs of this type are exactly the irreducible but not strongly irreducible systems, the last open case between the strongly irreducible systems settled by B\'ar\'any--Hochman--Rapaport and the reducible systems of the self-affine carpet literature.
Under a projective exponential separation condition, we show that the Hausdorff dimension of the attractor equals its affinity dimension whenever the affinity dimension is at most 2− \lambda_1/\lambda_2, where \lambda_2 < \lambda_1 < 0 are the Lyapunov exponents of the equilibrium state. The talk is based on a joint work with Demi Allen, Antti K\"aenm\"aki, K\'aroly Simon, and Sascha Troscheit.
10月23日(金) Tamara Kucherenko氏 (The City College of New York),
Stochastic properties of the equilibrium states for H\"older potentials on coded shift spaces
Abstract:
A coded shift is the closure of all bi-infinite concatenations of words from a fixed countable generating set. It admits a natural decomposition into a concatenation set of genuine concatenations and a residual set arising from the closure. We prove uniqueness of equilibrium states for Hölder potentials when the pressure of the concatenation set dominates that of the residual set, and, under mild growth assumptions on the generating set, show that the resulting equilibrium state exhibits exponential decay of correlations, satisfies the central limit theorem, and obeys the law of the iterated logarithm. Notably, these statistical properties hold under considerably weaker hypotheses than uniqueness itself, and remain valid even when the equilibrium state is not unique. As an application, we establish all three properties for the (possibly non-unique) equilibrium states of Motzkin–Dyck shifts — new results even for measures of maximal entropy.
Philippe Thieullen氏（University of Bordeaux）
Ergodic optimization and the Frenkel-kontorova model
Abstract:
In ergodic optimization we try to characterize the structure of orbits of a dynamical system that minimize an observable in the mean. The theory is well developped for Lipschitz observables over a symbolic dynamical system with a finite alphabet. In the Frenkel-Kontorova model we try to characterize the structure of configurations of atoms over a one-dimensional lattice that minimize the total energy. The main difference is that the alphabet is now the set of real numbers. We will try to explain that minimizing orbits in both cases correspond to ground states configurations, that is configurations at the lowest energy level.
9月11日(金) 16:30から EKonstantin Mischaikow氏（Rutgers University）[応用数学セミナーと共催] (対面のみ)
Homological Dynamics
Abstract:
Frameworks for the analysis of nonlinear dynamics such as statistical mechanics or geometric methods focus on providing conceptual understanding and were developed before computation and direct use of data became ubiquitous in science and engineering. I will argue that the theory of the above mentioned frameworks is too rich, especially in the context of characterization of dynamics based on finite data sets.
This suggests the need for new frameworks and motivates the introduction of homological dynamics.
The name homological dynamics is meant to invoke an analogy: homological dynamics is to the geometric theory of dynamics as homological algebra is to algebraic topology. I will define a homological dynamical system and discuss the comparison between different homological dynamical systems and highlight obvious open problems. I will also describe how data driven dynamics can be translated into homological dynamics and how information from homological dynamics can be translated to the setting of continuous dynamics.
7月24日(金) 山下美紀 氏(熊本大学)
Weak Gibbs measures on shift spaces induced by certain mod 1 transformations
アブストラクト
For an increasing continuous function $f$ on $[0,1]$, a mod 1 transformation of $f$ is defined by $T_f(x)=f(x) \pmod 1$. In this talk, we consider the natural extension $\Sigma_f$ of the shift space induced by the mod 1 transformation $T_f$ satisfying some assumptions. We provide a necessary and sufficient condition under which any equilibrium measure for a potential function with bounded total oscillations on $\Sigma_f$ is a weak Gibbs measure.
7月17日(金) 山本航大 氏(九州大学)
C^1-robust heterodimensional tangencies
アブストラクト
微分同相写像が不安定次元の異なる2つのサドル周期点をもち，それらの安定多様体と不安定多様体が互いに交わってサイクルを形成するとき，heterodimensional cycleをもつという．これは3次元以上の力学系に現れる代表的な非双曲現象の一つである．2つのサドル周期点の不安定次元が異なるため，heterodimensional cycleを構成する2つの交点のうち，一方は擬横断的交差，他方は横断的交差となる．Bonatti-Díaz（2008）はこの種のheterodimensional cycleがC^1-robustであることを示した．これに対し，桐木-相馬（2012）は，横断的交差の代わりに接触を含むheterodimensional cycleからC^2-robust heterodimensional tangencyの存在を示した．しかし，C^1-robust heterodimensional tangencyについては扱われなかった．本講演では，接触を含むheterodimensional cycleから，C^1-robust heterodimensional tangencyが存在することを紹介する．本研究は桐木紳氏（東海大学）との共同研究である．
6月19日(金) 富澤俊太朗 氏(東京大学)
Infinitely Many Attracting Periodic Circles in Higher Dimensions
アブストラクト
We study C^r (5 ≦ r ≦ ∞) diffeomorphisms on closed manifolds of dimension at least three with a heteroclinic cycle between two hyperbolic periodic points.
At each point, the unstable direction is one dimensional, and the stable and unstable eigenvalues closest to 1 in modulus are real and simple. One heteroclinic connection is transverse and the other is non-transverse, and the product of those two eigenvalues is less than 1 at one point and greater than 1 at the other. Arbitrarily close to such a map, there are open sets in which a residual subset of diffeomorphisms has infinitely many attracting normally hyperbolic periodic circles.
6月12日(金) 16:30から EEric Bedford 氏 (Stony Brook University)ric Bedford氏
Real and complex dynamics of a rational mapping of the plane
Abstract:
We consider the rational mapping of the plane that arises in the renormalization of the iterated monodromy group of the Basilica map. This is related to the so-called family of spectral measures. We will discuss the dynamical properties of this map from the real and complex points of view.
5月15日(金) 原誠人 氏(京都大学)
台風の応用力学系に向けて
アブストラクト
台風に代表される大規模な気象系に人工的な介入を行って激甚災害を回避することは，将来的な実現が待望される技術的挑戦である．しかしこうした問題には，系の規模に対して可能な介入量・介入パターンがごく限定的であること，制御の前提となるべき予測がそもそも困難であること，といった基礎的な難問が避けがたく伴う．そのため，高効率な制御や高精度な予測の実現，あるいは制御・予測の原理的限界の解明に寄与する数理的考察が期待されている．本講演では，そのための予備的観察と言うべき二つの共同研究について主に紹介する．具体的には，2次元熱対流（モデル）の制御とその最適制御パターンに関する考察（主著者：堤夏輝氏），および台風（モデル）の発生時刻のリザバー計算による予測とそれに関連する実験等（主著者：神野拓哉氏）に関して議論したい．（現時点では数値結果が主であり，スライドショーによる発表になることをご了承ください．）
世話人：
柴山 允瑠(京都大学)
梶原 唯加(京都大学)