Permanent Faculty: Lorenzo Justiniano Díaz Casado

Lorenzo Justiniano Díaz Casado

PhD, IMPA, Rio de Janeiro,RJ-Brasil, 1990
Office: 876
Position: Full Professor
Phone: (21) 3527-1742
E-mail: lodiaz
Dynamical Systems

Lattes CV | Personal Homepage

LJD (Madrid, 1961) obtained his undergraduate and master degree from Universidade Complutense de Madrid (1994). In 1990 he obtained his PhD from IMPA under the guidance of Jacob Palis. His research area is Dynamical Systems Theory and Ergodic Theory with particular emphasis in the studies of bifurcation phenomena via cycles, generic dynamics, and topological and ergodic aspects of elementary pieces of dynamics. He is full professor at PUC-Rio, member of the Academia Brasileira de Ciências (since 2012) and The World Academy of Sciences (TWAS) (since 2018). He was invited speaker of the session Dynamical Systems and Ordinary Differential Equations (ICM 2018). He was coordinator and vice-coordinator of the Mathematics section of the Brazilian agency CAPES (2015-18 and 2012-15, respectively). Currently he is executive editor of the Ergodic Theory and Dynamical Systems, member of the editorial boards of Nonlinearity, Projeto Euclides IMPA, and IOP-ebooks. He is co-founder of the inter-institutional seminar EDAI (Encontros de Dinâmica Além Instituições) in collaboration with UFRJ and UFF and of the seminars Oktobermat and Seminário q.t.p at PUC-Rio that are dedicated to general audience.

Research Results

The recent research by LJD considers the following topics. Construction of non-hyperbolic ergodic measures (i.e. with some zero Lyapunov exponent) and applications of these techniques to describe the space of ergodic measures in non-hyperbolic settings and elliptic cocycles em SL(2,Z). He also uses these techniques for developing the thermodynamical formalism of some representative classes of non-hyperbolic systems (skew products and partially hyperbolic systems). He also studies paradigmatic examples of non-hyperbolic systems, as the so-called porcupine-like horseshoes and their variations. Finally, he also continues the study of the bifurcation via heterodimensional cycles, paying attention to heterodimensional and homoclinic tangencies and cycles of co-index greater than one,