25 citations · 26 across the 8 of their papers we have counts for
13 papers
Robustness of topological entropy under small area deformations
Marcelo R. R. Alves, Matthias Meiwes, Beomjun Sohn
In this paper, we establish a new type of stability phenomenon for the topological entropy of Hamiltonian diffeomorphisms of closed surfaces. For a closed surface endowed with an a…
Polytopes and -Riemannian metrics with positive
Marcelo R. R. Alves, Matthias Meiwes
We study Reeb dynamics on starshaped hypersurfaces in arising as smoothings of starshaped polytopes. Using the --stability of positive topological entropy for R…
From curve shortening to flat link stability and Birkhoff sections of geodesic flows
Marcelo R. R. Alves, Marco Mazzucchelli
We employ the curve shortening flow to establish three new results on the dynamics of geodesic flows of closed Riemannian surfaces. The first one is the stability, under -smal…
C^0-stability of topological entropy for Reeb flows in dimension 3
Marcelo R. R. Alves, Lucas Dahinden, Matthias Meiwes +1
We study stability properties of the topological entropy of Reeb flows on contact 3-manifolds with respect to the C^0-distance on the space of contact forms. Our main results show…
Braid stability and the Hofer metric
Marcelo R. R. Alves, Matthias Meiwes
In this article we show that the braid type of a set of -periodic orbits of a non-degenerate Hamiltonian diffeomorphism on a surface is stable under perturbations which are suff…
-Robustness of topological entropy for geodesic flows
Marcelo R. R. Alves, Lucas Dahinden, Matthias Meiwes +1
In this paper, we study the regularity of topological entropy, as a function on the space of Riemannian metrics endowed with the topology. We establish several instances of e…
Entropy collapse versus entropy rigidity for Reeb and Finsler flows
Alberto Abbondandolo, Marcelo R. R. Alves, Murat Saglam +1
On every closed contact manifold there exist contact forms with volume one whose Reeb flows have arbitrarily small topological entropy. In contrast, for many closed manifolds there…
Reeb orbits that force topological entropy
Marcelo R. R. Alves, Abror Pirnapasov
We develop a forcing theory of topological entropy for Reeb flows in dimension . A transverse link in a closed contact -manifold is said to force topological entr…
Dynamically exotic contact spheres in dimensions
Marcelo R. R. Alves, Matthias Meiwes
We exhibit the first examples of contact structures on with and on , all equipped with their standard smooth structures, for which every Reeb fl…
Topological entropy for Reeb vector fields in dimension three via open book decompositions
Marcelo Alves, Vincent Colin, Ko Honda
Given an open book decomposition of a contact three man-ifold (M, ) with pseudo-Anosov monodromy and fractional Dehn twist coefficient c = k n, we construct a Legendrian knot $Λ…
Positive topological entropy for Reeb flows on 3-dimensional Anosov contact manifolds
Marcelo R. R. Alves
Let be a compact contact 3-manifold and assume that there exists a contact form on whose Reeb flow is Anosov. We show this implies that every Reeb flow on $…
Legendrian contact homology and topological entropy
Marcelo R. R. Alves
In this paper we study the growth rate of a version of Legendrian contact homology, which we call strip Legendrian contact homology, in 3-dimensional contact manifolds and its rela…
Cylindrical contact homology and topological entropy
Marcelo R. R. Alves
We establish a relation between the growth of the cylindrical contact homology of a contact manifold and the topological entropy of Reeb flows on this manifold. We show that if a c…