The PI has proved, with Mark Demers, existence and mixing of the measure of maximal entropy of the map associated to the 2D periodic Lorentz gas.
Still with Mark Demers, the PI studied the thermodynamic formalism for the 2D periodic Lorentz gas, for a family of potential related to the unstable Jacobian. Then, with the PhD student Jérôme Carrand and Mark Demers, the PI proved existence and mixing of the measure of maximal entropy of the flow associated to the 2D periodic Lorentz gas. This uses a study by the second PhD student Jérôme Carrand of thermodynamic formalism for the 2D periodic Lorentz gas, for a family of potential related to the first collision time.
The first PhD Student, Malo Jézéquel, has been able to control the growth of dynamical determinants and zeta functions of differentiable (non analytic) maps and flows, with applications to the global trace formula. (Revisiting the Milnor--hurston kneading theory to obtain nuclear power decompositions in the non-analytic setting.)
With a Postdoc (Juho Leppänen), the PI has studied fractional response and fractional susceptibility function for transversal families of piecewise expanding maps.
With Daniel Smania, the PI has obtained pioneering results on the fractional susceptibility function for the quadratic family. With Magnus Aspenberg and Tomas Persson, the PI has proved an almost sure invariance principle for the quadratic family
The postdocs (Leppänen, Sedro, Selley, Castorrini, Korepanov, and Wormell) obtained results on central limit theorems with a rate of convergence for time-dependent intermittent maps, quadratic response, and differentiability and non-monotonicity of the rotation number, conditional mixing in deterministic chaos, speed of mixing for the measure of maximal entropy of Sinai billiards, .
36 articles have been published and 5 were submitted. One workshop, one conference, one school, and one smaller meeting were organised.
