Spectral rigidity of contact 3D Axiom A flows

Abstract: We show a rigidity result for two 3-dimensional contact Axiom A flows. More precisely, if the restriction of the flows to some basic set is orbit equivalent and iso-length-spectral, then the dynamics on the basic sets are conjugated through a homeomorphism of class $C^{1,\beta}$, in Whitney sense, for some $\beta\in(0,1)$, which also preserves the contact structures. The ideas are reminiscent of the work of Otal. As a consequence, interesting spectral rigidity results can be deduced for $C^k$ open dispersing billiards. This is a joint work with Martin Leguil.

mathematical physicsclassical analysis and ODEsdynamical systemsnumerical analysisprobabilitysymplectic geometry

Audience: researchers in the topic

Third DinAmicI Day

Series comments: The Giornata DinAmica (DAI Day) of the DinAmicI, the Community of Italian Dynamicists, takes place every two years and includes, in addition to scientific seminars, the assembly of members.

One of the aims of the DinAmicI is to promote young researchers: at least half of the invited speakers are in the early stage of their careers.

This third edition of the Day is exceptionally held online due to the restrictions caused by Covid and, exceptionally, the talks will be distributed over two afternoons.