Hausdorff dimension for non-hyperbolic repellers II: DA diffeomorphisms
Vanderlei Horita Marcelo Viana
Discrete & Continuous Dynamical Systems - A 2005, 13(5): 1125-1152 doi: 10.3934/dcds.2005.13.1125
We study non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomorphisms with unstable dimension 2 through a Hopf bifurcation. Using some recent abstract results about non-uniformly expanding maps with holes, by ourselves and by Dysman, we show that the Hausdorff dimension and the limit capacity (box dimension) of the repeller are strictly less than the dimension of the ambient manifold.
keywords: Repeller. Dimension theory Non-uniform hyperbolicity
Existence and uniqueness of maximizing measures for robust classes of local diffeomorphisms
Krerley Oliveira Marcelo Viana
Discrete & Continuous Dynamical Systems - A 2006, 15(1): 225-236 doi: 10.3934/dcds.2006.15.225
We prove existence of maximal entropy measures for an open set of non-uniformly expanding local diffeomorphisms on a compact Riemannian manifold. In this context the topological entropy coincides with the logarithm of the degree, and these maximizing measures are eigenmeasures of the transfer operator. When the map is topologically mixing, the maximizing measure is unique and positive on every open set.
keywords: Entropy maximizing measure non-uniform hyperbolicity.
Daniel Smania Ali Tahzibi Marcelo Viana
Discrete & Continuous Dynamical Systems - A 2007, 17(2): i-ii doi: 10.3934/dcds.2007.17.2i
This special issue of DCDS is dedicated to Carlos Gutierrez and Marco Antonio Teixeira, on the occasion of their 60th birthday.
    Born in Peru, C. Gutierrez obtained his Ph.D. degree from IMPA in 1974, under the supervision of Jorge Sotomayor. In the same year he began to serve as a researcher there. He retired from IMPA and now is a full professor at ICMC-University of São Paulo (USP), where his leadership has been crucial to the development of the research on dynamical systems.

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