Speakers: Yiming Ding, Łukasz Cholewa, Yun Sun, Ziyu Liu, Thiago de Paiva Souza, Jorge Olivares-Vinales, Eran Igra
Organizer: Eran Igra
Time: Friday, Dec. 19, 2025
Location: Room 1710
Zoom Meeting ID: 815 8854 6206 (Passcode: 866406)
Schedule:
10:30-11:20 – Yiming Ding
11:30-12:20 – Łukasz Cholewa
12:30 – 13:00 – Sun Yun
Lunch break
14:30 – 15:20 – Ziyu Liu
15:30 – 16:20 – Thiago de Paiva Souza
16:30 – 17:20 – Jorge Olivares Vinales
17:30 – 18:00 – Eran Igra
Titles and abstracts:
Title – Renormalization, complete invariants and parameterization of expansive Lorenz maps
Speaker – Yiming Ding (Wuhan University of Science and Technology)
Abstract: In this talk, we first introduce the definition of essential renormalizations. We also obtain the complete conjugacy invariants of expansive Lorenz maps. Given an expansive Lorenz map, there exists a unique cluster of points $(\beta_{i},\alpha_{i})$ in parameter space. As an application, we can define the distance of two expansive Lorenz maps, and investigate the uniform linearization of expansive Lorenz maps through periodic essential renormalizations.
Title – Renormalization in Lorenz Maps: Analytical and Symbolic Approaches
Speaker – Łukasz Cholewa (Krakow University of Economics)
Abstract: Lorenz maps are interval maps with a single discontinuity, which appear in a natural way as Poincare maps in geometric models of the well-known Lorenz attractor. Using both analytical and symbolic approaches, we study renormalizaions of Lorenz maps, i.e., certain return maps of a Lorenz map to smaller intervals around the discontinuity. The existence of renormalizations is closely related to the existence of completely invariant sets. This relation, however, turns out to be more delicate than the results in the literature indicate. It was believed that each renormalization corresponds to some completely invariant set that defines it, but in fact, for some of them, such a set does not exist. In this talk, we will present an algorithm to distinguish the renormalizations that can and cannot be recovered from completely invariant sets, and reveal the essence of the difference between them. This way, we complete the description of possible dynamics and provide a better insight into the structure of renormalizations in Lorenz maps. The talk will be based on joint work with Piotr Oprocha.
Title – Topologically expansive decreasing Lorenz maps with a hole at the discontinuity
Speaker – Yun Sun (Wuhan University of Technology)
Abstract: Let f be a topologically expansive decreasing Lorenz map and c be the discontinuity point. The survivor set is denoted as $S_{f}(H):=\{x\in[0,1]: f^{n}(x)\notin H, \forall n\geq 0\}$, where $H$ is an open subinterval. By combinatorial tools, we obtain the admissible condition for the kneading invariants of expansive decreasing Lorenz maps. Moreover, let $a$ be fixed, when $f$ has an ergodic a.c.i.m., we prove that the topological entropy function is a devil’s staircase. At the special case that f being a negative $\beta$-transformation, using the Ledrappier-Young formula, the Hausdorff dimension function is a devil’s staircase. All the results can be extended to the case that b is fixed.
Title: A multifractal analysis for Hoelder regularity of Gibbs measures on the real line
Speaker – Ziyu Liu (Dianji University)
Abstract: Gibbs measures on the real line provide various examples of singular measures. This talk aims to perform a multifractal analysis for Hoelder regularity of Gibbs measures on the real line. More precisely, we provide a formula for the Hausdorff dimension of the set of points at which the distribution function of the concerned Gibbs measure has finite alpha-Hoelder upper-derivative and positive alpha-Hoelder lower-derivative. The same formula was obtained in the multifractal analysis of quotients of Birkhoff sums by Pesin and Weiss (1997). We will discuss the relation between our result and the well-known results by Pesin and Weiss. This talk is based on the PhD thesis and one recent paper (DOI: 10.1016/j.jmaa.2025.129793) of the speaker.
Title: Knot Theory and Periodic Orbits of Flows
Speaker – Thiago de Paiva Souza (BICMR, Peking University)
Abstract: When the orbit of a flow on a 3-manifold returns to its initial point, it traces a simple closed curve—what dynamical systems call a periodic orbit and knot theorists naturally recognize as a knot. Knot theory provides powerful tools to distinguish, classify, and organize such periodic orbits.
In this talk, I will discuss how knot-theoretic techniques can be used to help classify and simplify flows in three-dimensional manifolds. While the discussion will remain at a general level, we will focus in particular on the periodic orbits arising from classical examples in dynamical systems, such as the Lorenz flow and the Smale horseshoe. These examples illustrate how knot theory reveals deep and unexpected connections between topology and dynamics. This perspective opens many new questions at the interface of these two fields, offering promising directions for future research.
Title: Non-existence of wandering intervals for asymmetric unimodal maps
Speaker – Jorge Olivares-Vinales (SCMS, Fudan University)
Abstract: A natural problem in dynamical systems is the classification of “equivalent” systems. In the real one-dimensional case, the ordering of the phase space (the circle or a compact interval) gives raise to the question when the order of the orbits of the systems determines it. More precisely, we can ask whether two maps which are combinatorially equivalent are topologically conjugated. This problem goes back to Poincare’s work dealing with circle homeomorphisms, and a positive answer depends on the non-existence of wandering intervals. In this talk, I will discuss a joint work with Professor Weixiao Shen from Fudan University, were we prove that an asymmetric unimodal map (i.e. with different left and right critical order) has no wandering intervals.
Title: Using Erdős’s methods to study Yorke’s problems
Speaker: Eran Igra (SIMIS)
Abstract: Consider an isotopy $f_t:M\to M$, where $M$ is some smooth manifold and $t\in[0,1]$. Assuming the dynamics of $f_0$ are “simple”, in how many different ways can it bifurcate and evolve into a “chaotic” regime where, say, $f_1$ has infinitely many periodic orbits? It is exactly this question we consider in this talk. Using graph theoretical tools we prove that when the dimension of $M$ is greater than $4$, there are infinitely many such ways. Conversely, in dimensions $1<d<4$ we will prove the answer to this question depends on how many $d$ dimensional systems are “essentially” $d-1$ dimensional ones. Based on a joint work with Valerii Sopin.
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