Tuesday, 10th November 2027
10:00 am, Seminari MA, Dept. IMAE
Víctor Sirvent (Universidad Católica del Norte, Chile): "Generalised Fibonacci shifts in the Lorenz attractor: dynamical, combinatorial and number-theoretic aspects"
Abstract: We study symmetric Lorenz attractors whose homoclinic loop has a well-ordered orbit. We show the symmetry implies a very regular behaviour on the dynamics in the topological and metric sense. Let ([-1,1],f) be the one-dimensional Lorenz map (obtained by reduction) having a well-ordered orbit and ([-1,0], f̃) be the quotient map, given by the equivalence relation x~-x. The dynamics of f̃ is described explicitly as a subshift of finite type which generalises the Fibonacci shifts, and this fact is used to compute topological entropy of f. Furthermore, we show that in general ([-1,0], f̃) is related to a factor of the k-bonacci shift. In particular we find that the one-dimensional Lorenz map replicates an interesting duplicating/unfolding behaviour of the k-bonacci shift found in a different context.
We also study the combinatorics of the Markov partition of the map that give rise to the previous shifts, including the associated integer sequences and substitutions, and number-theoretic properties of eʰ where h is the entropy of those shifts.
Wednesday, 11th November 2027
10:00 am, Seminari MA, Dept. IMAE
Claire David (Sorbonne Université, CNRS, France): "Phase Transitions in Loewner Evolution: The Weierstrass Drift"
Abstract: We introduce the Weierstrass Drift as a deterministic toy model for the Schramm–Loewner evolution process (SLE) driven by Brownian motion. More precisely, given T>0, we are interested in the solution g∶[0,T]×H → C of the chordal forward Loewner (partial) differential equation, where H={z=x+iy, Im(z)=y>0}. The now classical condition obtained by Joan Lind ensures that, if the Lip (1/2) norm of the drift is below 4, the resulting Loewner trace is a simple curve. We hereafter revisit this condition and obtain more general results. These results allow us to determine precise thresholds for phase transitions between simple and non-simple Loewner traces. Our general Weierstrass toy model could provide a better understanding of the singularities of multifractal SLE traces.
Thursday, 24th September 2026
12:00 am, Seminari MA, Dept IMAE
Abdennebi Omrane (Université de Guyane):
"Analysis and optimal control for a PDE problem in forest harvesting"
Abstract: Optimal control methods are used in many fields as in economics, physics, biology, engineering, etc. We present a partial differential model (PDE) in application to forest harvesting problems and timber production, where a control variable is incorporated. The control represents the cutting (trees) function. We consider an optimization criterion for the control of the timber production where the forest conservation is also taken into account. The mathematical model is nonlinear and the growth function and vital variables (fertility, mortality ..) are dependent of the environment (competition for light). We show the techniques used for proving the existence of a solution. We will see that the mathematical problem also admits an optimal control that we characterize by an optimality system using the Pontryagin maximum principle (PMP). Finally, we give some concluding remarks.
Short CV: Mr Abdennebi OMRANE is a Professor at the University of French Guiana (Université de Guyane) and a member of the research team: UMR EcoFoG (Ecologie des Forêts de Guyane). He obtained his doctorate in applied mathematics “Kinetic methods for multidimensional scalar conservation laws” at the University of Nice in 1998, and his Habilitation in 2006 at the University des Antilles et de la Guyane (UAG) on the “Analysis and optimal control of some PDE problems".