In this work we obtain a new criterion to establish ergodicity and non-uniform hyperbolicity of smooth measures of diffeomorphisms. This method allows us to give a more accurate description of certain ergodic components. The use of this criterion in combination with topological devices such as blenders lets us obtain global ergodicity and abundance of non-zero Lyapunov exponents in some context...

We perform a numerical study of the breakdown of hyperbolicity of quasi-periodic attractors in the dissipative standard map. In this study, we compute the quasi-periodic attractors together with their stable and tangent bundles. We observe that the loss of normal hyperbolicity comes from the collision of the stable and tangent bundles of the quasi-periodic attractor. We provide numerical eviden...

We consider the problem of realizing hyperbolicity cones as spectrahedra, i.e. as linear slices of cones of positive semidefinite matrices. The generalized Lax conjecture states that this is always possible. We use generalized Clifford algebras for a new approach to the problem. Our main result is that if −1 is not a sum of hermitian squares in the Clifford algebra of a hyperbolic polynomial, t...