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Talk 01 — Riddhi Shah (Jawaharlal Nehru University, New Delhi, India) — [computing…]Local time: click here to view in your time zoneTitle: Dynamics of action of automorphisms on the space of closed subgroups of Lie groups
Abstract
We consider the action of automorphisms of a connected Lie group on the compact space of all closed subgroups of it endowed with the Chabauty topology. This action keeps various proper subspaces invariant, e.g. the space of closed abelian subgroups, discrete cyclic subgroups or closed one-parameter subgroups.. We will study the dynamics of distal action as well as expansive action of automorphisms on these spaces and characterise them.
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Talk 02 — Sourav Bhattacharya (Visvesvaraya National Institute of Technology, Nagpur, India) — [computing…]Local time: click here to view in your time zoneTitle: Triod twist cycles and circle rotations
Abstract
We study the problem of relating cycles on a \emph{triod} $Y$ to \emph{circle rotations}. We prove that the simplest cycles on a \emph{triod}~$Y$ with a given \emph{rotation number}~$\rho$, called \emph{triod--twist cycles} are conjugate, via a piece-wise monotone map of \emph{modality} at most~$m + 3$, where~$m$ is the \emph{modality} of~$P$ to the rotation on~$S^1$ by angle~$\rho$, restricted to one of its cycles.
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Talk 03 — David Aulicino (Brooklyn College & The Graduate Center (CUNY), USA) — [computing…]Local time: click here to view in your time zoneTitle: Counting Saddle Connections on Slit Translation Surfaces
Abstract
A slit translation surface is a translation surface with a distinguished collection of saddle connections called slits. We consider hyperelliptic translation surfaces with a single slit invariant under the hyperelliptic involution. We consider the set of all saddle connections on this surface that are disjoint from the slit and establish its growth rate. The upper bound holds for every translation surface, while the lower bound holds for almost every translation surface in the stratum. All necessary background will be given. This is joint work with Howard Masur, Huiping Pan, and Weixu Su.
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Talk 04 — Rafael Lucena (Universidade Federal de Alagoas, Brasil) — [computing…]Local time: click here to view in your time zoneTitle: Thermodynamic Formalism and Statistical Properties for Discontinuous Partially Hyperbolic Systems
Abstract
We establish the existence and statistical properties of equilibrium states for a class of piecewise partially hyperbolic maps. By developing a specialized functional-analytic framework, we prove the regularity of disintegrations and the uniqueness of equilibrium states, bypassing traditional requirements for local invertibility or global smoothness. Under this framework, we derive several limit theorems, including exponential decay of correlations, the Central Limit Theorem, and quantitative statistical stability. The versatility of our approach is demonstrated through applications to non-invertible systems admitting semi-conjugacy to intermittent maps (e.g., Manneville-Pomeau) and fat solenoidal attractors. This is joint work with Rafael Bilbao.
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Talk 05 — Alex Blumenthal (Georgia Tech, USA) — [computing…]Local time: click here to view in your time zoneTitle: Instability of invariant manifolds for iterated function systems
Abstract
Invariant manifolds play a pivotal role in a variety of models of practical interest, e.g., those coming from physics for which the stabilizer set of a given symmetry subgroup is invariant. A guiding example comes from degenerately forced fluids models, where as parameters are varied the physical measure of the system can spontaneously lose symmetries of the background forcing. Determining the instability of invariant sets can be an intractably hard problem for a variety of reasons, including complexity of the dynamics along the invariant set (e.g., coexistence phenomena) as well as other tricky global obstructions (e.g., the figure eight attractor). For systems subject to noise, these challenges are far more tractable, as noise has a tendency to regularize asymptotic statistics and enforces ergodicity under checkable conditions. In this talk I will discuss recent work with Jacob Bedrossian and Sam Punshon-Smith on the use of Lyapunov exponents and ergodic theory tools for establishing instability of almost-surely invariant sets for iterated function systems.
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Talk 06 — Darren Creutz (Vanderbilt University, USA) — [computing…]Local time: click here to view in your time zoneTitle: Word complexity cutoffs for measure-theoretic properties in symbolic dynamics
Abstract
Given a symbolic dynamical system, there is a natural measure of complexity--word complexity--which is more fine-grained than entropy and can distinguish classes of zero entropy systems. Remarkably, word complexity (which is not preserved under measure isomorphism) exactly captures the complexity at which various measure-theoretic properties can manifest: for instance, strong mixing can occur with word complexity arbitrarily close to linear but cannot occur in the linear word complexity regime [C '26 TAMS]. The talk will explain word complexity and the various cutoffs that have been established, largely on my own results (some joint with R. Pavlov and some joint with T. Adams) and mentioning related results of Cyr-Kra and Espinosa.
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Talk 07 — Barbara Shipman (University of Texas at Arlington, USA) — [computing…]Local time: click here to view in your time zoneTitle: From Euclidean to Lorentzian Phase Space
Abstract
The Lorentz numbers, also known as the hyperbolic numbers, offer a new and interesting phase space for dynamical systems. They have the form a + bτ, where a and b are real and the square of τ is 1 (but τ is not 1 or -1). In the Lorentz numbers, the unit circle of the complex plane is replaced by a unit hyperbola, the Cauchy-Riemann equations are replaced by the Lorentz-Cauchy-Riemann equations, and the Laplace equation is replaced by the wave equation. In contrast to the complex numbers, the Lorentz numbers contain zero divisors, which appear along the light cone; factorization of polynomials is not unique, and polynomials of degree n can have more than n distinct roots!
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Talk 08 — Philipp Kunde (Oregon State University, USA) — [computing…]Local time: click here to view in your time zoneTitle: Almost sure results on the closeness of orbits
Abstract
Motivated by the study of patterns in DNA sequences and random processes, the so-called Longest Common Substring Problem seeks to identify the largest block of coincidence between two symbolic sequences. As a variant of this classical problem in information theory, we consider the minimal distance between orbits of measure-preserving dynamical systems. In the spirit of dynamical shrinking target problems we identify distance rates for which almost sure asymptotic closeness properties can be ensured. More precisely, we consider the set $E_n$ of pairs of points $x,y$ whose orbits up to time $n$ have minimal distance to each other less than the threshold $r_n$. If $(r_n)_n$ shrinks sufficiently slowly, almost every pair $x, y$ will meet this condition for all large enough $n$, i.e., $(\mu\times \mu)(\limsup_n E_n)=1$. On the other hand, if $(r_n)_n$ shrinks too quickly, then the measure of this set is zero. In joint work with Mike Todd, Maxim Kirsebom, and Tomas Persson, we obtain bounds on the sequence $(r_n)_n$ to guarantee that $\limsup_{n}E_n$ and $\liminf_{n} E_n$ are sets of measure 0 or 1.
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Talk 09 — Chris Johnson (Western Carolina University, USA) — [computing…]Local time: click here to view in your time zoneTitle: Generalized periodic points of abelian differentials on torus covers
Abstract
The moduli space of abelian differentials in a fixed genus is stratified by the number and orders of the zeros of the differential. Marking points introduces additional strata, which form surface bundles over the underlying unmarked strata. This perspective allows us to define a notion of generalized periodic points lying in the fibers of these bundles, despite the absence of a natural group action on the fibers. Work of Eskin, Filip, and Wright shows that fibers over torus covers contain infinitely many such generalized periodic points. In this talk, I will describe joint work with Chris Judge in which we prove that the number of points of bounded period on torus covers grows at most quartically in the period, refining a previous result of Gutkin, Hubert, and Schmidt.