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Research Results LORENZO J. DIAZ 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 paying special attention to the so-called porcupine-like horseshoes. Finally, he also continues the study of the bifurcation via heterodimensional cycles, paying attention to heterodimensional tangencies and cycles of co-index two. * Weak* and entropy approximation of nonhyperbolic measures: a geometrical approach (com K. Gelfert e B. Santiago) Math. Proc. Cambridge Phil. Soc. (to appear). * Nonhyperbolic step skew-products: Entropy spectrum of Lyapunov exponents (com K. Gelfert e M. Rams) Comm. in Math. Phys. 367 (2019) 351-416. * A criterion for zero averages and full support of ergodic measures (com Ch. Bonatti e Jairo Bochi), Moscow Math. J. 18 (2018) 15-61. * What is a blender? (com Ch. Bonatti, S. Crovisier, A. Wilkinson). Notices Amer. Math. Soc. 63 (2016) 1175-1178. * Robust criterion for the existence of nonhyperbolic ergodic measures (com J. Bochi e Ch. Bonatti). Comm. in Math. Phys. 344 (2016) 751-795. |
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(Updated 11/18/2019) |
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| Mathematics Department / PUC-Rio Rua Marquês de São Vicente, 225 - Edifício Cardeal Leme, sala 862 - Gávea - Rio de Janeiro - CEP 22451-900 Telefones: (+55-21) 3527-1280, (+55-21) 3527-1281, Fax: (+55-21)3527-1282 |
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