Bernardo Carvalho

My research program is dedicated to the exploration and advancement of mathematical knowledge, with a particular focus on Dynamical Systems. One of my primary research goals is to develop further chaos theory and hyperbolic dynamics and study relations between chaotic and hyperbolic systems. More precisely, study the interfaces between hyperbolic dynamics, topological dynamics, and fractal geometry. I have been exploring the dynamics of Anosov diffeomorphisms, the dynamics beyond topological hyperbolicity, and the fractal structures of hyperbolic graphs.