5 problems

Consider volume-preserving partially hyperbolic systems, meaning systems preserving a volume and admitting a partially hyperbolic invariant splitting. Generic exponential mixing co…

The multidimensional Lorenz attractor is the sectional-hyperbolic attractor introduced by Bonatti, Pumariño and Viana. Multidimensional Lorenz mixing conjecture. The multidimension…

Let a singular flow admit equilibrium states associated to Hölder continuous potentials. Equilibrium-state mixing conjecture. The techniques of Tsujii and Zhang can be adapted to s…

Let an ergodic physical probability measure be supported on a non-trivial singular-hyperbolic attracting set. Uniform non-integrability conjecture. The Uniform Non-Integrability (U…

Let an expanding semiflow be given together with its stable leaves and an original flow to which a skew-product model may be semiconjugated. Exponential mixing skew-product conject…