12 citations · 15 across the 7 of their papers we have counts for
9 papers · 1 filter
Mostow rigidity for skew solenoidal manifolds
Fernando Alcalde Cuesta, Matilde Martínez, Alberto Verjovsky
We prove a Mostow rigidity theorem for foliated bundles over closed hyperbolic manifolds of dimension endowed with a completely invariant measure of full support. These…
Free minimal actions of solvable Lie groups which are not affable
Fernando Alcalde Cuesta, Álvaro Lozano Rojo, Matilde Martínez
We construct an uncountable family of transversely Cantor laminations of compact spaces defined by free minimal actions of solvable groups, which are not affable and whose orbits a…
Unique ergodicity of the horocycle flow on Riemannnian foliations
Fernando Alcalde Cuesta, Françoise Dal'Bo, Matilde Martínez +1
A classic result due to Furstenberg is the strict ergodicity of the horocycle flow for a compact hyperbolic surface. Strict ergodicity is unique ergodicity with respect to a measur…
Insertion-tolerance and repetitiveness of random graphs
Fernando Alcalde Cuesta, Álvaro Lozano Rojo, Antón C. Vázquez Martínez
Bond percolation on Cayley graphs provides examples of random graphs. Other examples arise from the dynamical study of proper repetitive subgraphs of Cayley graphs. In this paper w…
Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology
Fernando Alcalde, Françoise Dal'Bo, Matilde Martínez +1
We consider a minimal compact lamination by hyperbolic surfaces. We prove that if it admits a leaf whose holonomy covering is not topologically trivial, then the horocycle flow on…
Remarks on the dynamics of the horocycle flow for homogeneous foliations by hyperbolic surfaces
Fernando Alcalde Cuesta, Françoise Dal'Bo
This article is a first step towards the understanding of the dynamics of the horocycle flow on foliated manifolds by hyperbolic surfaces. This is motivated by a question formulate…
A geometric proof of the Affability Theorem for planar tilings
Fernando Alcalde Cuesta, Pablo González Sequeiros, Álvaro Lozano Rojo
We give a geometric proof of the Affability Theorem of T. Giordano, H. Matui, I. Putnam and C. Skau for aperiodic and repetitive planar tilings.
Averaging sequences
Fernando Alcalde Cuesta, Ana Rechtman
In the spirit of Goodman-Plante average condition for the existence of a transverse invariant measure for foliations, we give an averaging condition to find tangentially smooth mea…
Minimal Følner foliations are amenable
Fernando Alcalde Cuesta, Ana Rechtman
For finitely generated groups, amenability and Følner properties are equivalent. However, contrary to a widespread idea, Kaimanovich showed that Følner condition does not imply ame…