Jorge Rocha's Annual Report

Jorge Rocha's Annual Report

Year: 

2015

Brief description of the research activities: 

In a join work with Lorenzo Diaz (PUC-RJ) and Salete Esteves (IPB) we introduce a two-parameter family of ‘partially hyperbolic’ skew products where one of them describes the unfolding of a heterodimensional cycle and the other  measures the ‘central distortion’ of the systems. This family displays some of the main characteristic properties of the unfolding of heterodimensional cycles as hyperbolic dynamics,  intermingled homoclinic classes of different indices and secondary bifurcations via collision of hyperbolic homoclinic classes. The central dynamics is described using a one-dimensional family of iterated function systems. (in press)

In a join work with Mário Bessa (UBI), Célia Ferreira (CMUP) and Paulo Varandas (UFBA) we contribute to the generic theory of Hamiltonians by proving that there is a C2-residual R in the set of C2 Hamiltonians on a closed symplectic manifold M, such that, for any H of R, there is a full measure subset of energies e in H(M) such that the Hamiltonian level (H,e) is topologically mixing; moreover these level sets are homoclinic classes. (in press)

Talks / Seminars / Courses : 

Speakers
Jorge Rocha