• Rencontre de Systèmes dynamiques à l'IMB de Bordeaux, 1-2 décembre 2025, salle 385, 50 mn talk + 10 min question. Pour arriver à l'Institut, vous pouvez vous référer à la page cliquer ici.
  • Schedule

    	Lundi	mardi
    8:00 - 9:00	Samuel Petite	Gael Meignan
    9:00 - 10:00	Leo Gayral	Nicolas Gourmelon
    10:00 - 10:30	break	break
    10:30 - 11:30	Sandro Vaienti	Jasmin Raissy
    11:30 - 12:30	Elise Goujard	Philippe Thieullen
    12:30 - 14:00	lunch	lunch
    14:00 - 15:00	Mathieu Sablik
    15:00 - 16:00	Jiayun QI
    16:00 - 16:30	break
    16:30 - 17:30	Mickael Matusinski
    17:30 - 18:30	Matias Zimmermann

  • Speakers:
    • Leo Gayral (Université de Nancy)
      Title: Computer-Powered Chaos in Lattice Models
      Abstract: The study of combinatoric properties of tilings on lattice models has a long history of interactions with both computability (e.g. the undecidability of the domino problem) and statistical physics (e.g. the Peierls argument), but the joining of those two interfaces is relatively recent. Notably, the question “chaotic temperature dependence” originates from the spin-glass literature, and has been active for the last two decades.
      
      In this context, chaoticity can be summarised as the fact that no converging behaviour can occur in a given model as its temperature goes to 0. First formally established for an infinite spin alphabet, this property was later refined using a finite alphabet with long-range 1D interactions, and then finite-range interactions in higher dimensions.
      
      In this talk, I will notably focus on how the simulation of Turing machines within tilings has played a key role in this evolution, up to and including a realisation result on the zero-temperature limit accumulation sets of chaotic models.
    
    
    • Elise Goujard (Université de Bordeaux)
      Title: An introduction to dynamics of polygonal billiards
      Abstract: I will review some recent results about the dynamics of polygonal billiards, focusing mostly on rational polygons. In this case the dynamical properties of the billiard are related to dynamical and geometric properties of corresponding flat surfaces and their moduli space.
    
    
    • Nicolas Gourmelon (Université de Bordeaux)
      Title: Tous les difféomorphismes sont renormalisations totales de difféomorphismes proches de l'identité
      Abstract: Ceci est une collaboration avec Pierre Berger et Mathieu Helfter. Nous montrons que toute dynamique isotope à l'identité existe arbitrairement proche de l'identité, répondant ainsi à des questions de Takens-Ruelle, Turaev, Katok-Thouvenot.
      
      Nous formalisons cela en une notion de renormalisation {\em totale}, dont un exemple élémentaire est l'induction de Rauzy. Nous construisons un ouverts de difféomorphismes totalement renormalisables sur les variétés $V$ de la forme $\mathbb R/\mathbb Z \times M$.
      
      En concaténant ces difféomorphismes par chirurgies, on obtient un groupe $\mathbf P$ de difféomorphismes qui sont renormalisations totales de perturbations de $\mathrm{Id}_V$. On lui associe une l'algèbre de Lie (de dimension infinie) dont l'étude montre que $\mathbf P=\mathrm{Diff}_0(V)$.
    
    
    • Mickael Matusinski (Université de Bordeaux)
      Title: Non oscillating trajectories of o-minimal vector fields in dim 3
      Abstract: In the context of a polynomially bounded o-minimal structure over the field of real numbers, we consider a system of two non autonomous differential equations. We show that two non oscillating solutions of such system that have flat contact and with a regular separation property (in the sense of Lojasiewicz) are either interlaced, or else have their coordinates belonging to a common Hardy field.
      
      This dichotomy generalizes some of the results from F. Cano, R. Moussu and F. Sanz about non oscillating trajectories of real analytic vector fields in dimension 3 (dichotomy for integral pencil of trajectories), and from O. Le Gal, P. Speissegger and F. Sanz about solutions of o-minimal linear differential systems. After introducing the notions and context, if time permits we'll give a sketch of the proof.
      
      This is a joint work with O. Le Gal and F. Sanz.
    
    
    • Gael Meignan (Université de Bordeaux)
      Title: Mather's beta function and Lipschitz bound of minimizing configurations
      Abstract: We investigate the Aubry-Mather model with twist interaction. We ask ourself how we can link the average action to the Lipschitz bound of minimizing configuration ? We provide also a uniform bound for this Lipschitz constant for configurations with rotation number in a compact subset. Then, we present several results linked to Senn's articles.
    
    
    • Samuel Petite (Université d'Amiens)
      Title: Language stable shifts
      Abstract: language stable shifts form a rich class of shifts that was recently introduced by V. Cyr and B. Kra. This family contains many classical examples of subshifts, of various complexities ranging from systems of strictly positive entropy, such as subshift finite-type (SFT), to systems of low complexity, such as shifts of linear complexity. They are generic among the family of shifts. In this talk, we present some of their properties, in particular those concerning the cellular automata preserving them and their invariant measures.
    
    
    • Jianyun QI (Université de Bordeaux)
      Title: Spectral Methods for the Pressure (following Hautecoeur, Guivarc’h and Le Page)
      Abstract: We study transfer operators arising from random products of matrices. Starting from the Ruelle operator $L_\beta$, we construct a Markov operator $Q_\beta$ using Doob's relativisation procedure. Under an irreducibility condition, we establish a Doeblin--Fortet inequality for $Q_\beta$ and deduce that $Q_\beta$ is quasi-compact on a H\"older space. This implies the quasi-compactness of $L_\beta$ as well. These results are taken from Hautecoeur's paper and provide an analytic tool for understanding the pressure function.
    
    
    • Jasmin Raissy (Université de Bordeaux)
      Title: Holomorphic dynamics in dimension 2 and geometry of surfaces
      Abstract: In this introductory lecture I will present the connections between the dynamics of germs of biholomorphisms of $\mathbb{C}^2$ tangent to the identity at a fixed point, the real-time dynamics of homogeneous vector fields in $\mathbb{C}^2$ and the dynamics of the geodesic flow on affine surfaces, focusing on new results and open problems.
    
    
    • Mathieu Sablik (Université de Toulouse)
      Title: A study of phase diagrams for perturbed cellular automata
      Abstract: The perturbed counterpart of a cellular automaton $F$ is obtained by modifying each cell independently with probability $\epsilon$ and choosing the new value uniformly after each iteration of $F$. Denote the perturbed cellular automaton with noise parameter $\epsilon$ by $F\epsilon$. We consider two natural questions:
      
      - For which set of parameters does $F\epsilon$ admit a unique invariant measure?
      - Which set of invariant measures are selected when $\epsilon$ goes to 0?
      
      We will consider these questions in relation to specific examples and attempt to describe the possible sets that can be reached.
    
    
    • Philippe Thieullen (Université de Bordeaux)
      Title: Maximizing measures of generic matrix cocycles
      Abstract:
    
    
    • Sandro Vaienti
      Title:Conditional limit theorems for hyperbolic systems
      Abstract:We consider a class of hyperbolic diffeomorphisms with a hole. We characterize the convergence to the equilibrium state on the surviving set by distributional limit theorems describing the behavior of trajectories under the condition that they remain outside the hole for a finite time.
    
    
    • Matias Zimmermann (Université de Bordeaux et UNICAMP-Brésil))
      Title: Thermodynamic Formalism and Ergodic Optimization for Random Subshifts of Finite Type
      Abstract: In this talk, we explore the extension of classical thermodynamic formalism to random dynamical systems defined on symbolic spaces with unbounded finite alphabets. Furthermore, we investigate the 'zero temperature' limit ($\beta \to \infty$) to link thermodynamic formalism with ergodic optimization. Focusing on the specific case of 2-step random subshifts, where the interaction energy is defined by a random matrix, we demonstrate that the log-scaled eigenfunctions of the Ruelle operator converge, as the temperature vanishes, to calibrated subactions, effectively selecting the minimizing measures (ground states) of the system.