10 papers
Isospectral Reductions of Non-negative Matrices
Alexandre Baraviera, Pedro Duarte, Longmei Shu +1
Isospectral reduction is an important tool for network/matrix analysis as it reduces the dimension of a matrix/network while preserving its eigenvalues and eigenvectors. The main c…
Billiards in generic convex bodies have positive topological entropy
Mário Bessa, Gianluigi Del Magno, João Lopes Dias +2
We show that there exists a open dense set of convex bodies with smooth boundary whose billiard map exhibits a non-trivial hyperbolic basic set. As a consequence billiards in…
Isospectral Reduction in Infinite Graphs
Pedro Duarte, Maria Joana Torres
L. A. Bunimovich and B. Z. Webb developed a theory for transforming a finite weighted graph while preserving its spectrum, referred as isospectral reduction theory. In this work we…
On shadowing and hyperbolicity for geodesic flows on surfaces
Mario Bessa, Maria Joana Torres, Joao Lopes Dias
We prove that the geodesic flow on closed surfaces displays a hyperbolic set if the shadowing property holds C2-robustly on the metric. Similar results are obtained when considerin…
Eigenvectors of isospectral graph transformations
Pedro Duarte, Maria Joana Torres
L.A. Bunimovich and B.Z. Webb developed a theory for isospectral graph reduction. We make a simple observation regarding the relation between eigenvectors of the original graph and…
r-Regularity
Pedro Duarte, Maria Joana Torres
We provide a characterization of r-regular sets in terms of the Lipschitz regularity of normal vector fields to the boundary.