19 citations · 31 across the 7 of their papers we have counts for
8 papers
Holomorphic Linear $\C^k$-Actions, Trace Foliations, and Higher-Rank Poincaré Dynamics
Aubin Arroyo, Carlos Cabrera, José Seade +1
We study the orbit decomposition on $\C^n$ generated by diagonal holomorphic $\C^k$-actions in the higher-rank setting of the classical Poincaré--Siegel dichotomy for linear vector…
Hausdorff dimension of sets of numbers with large Lüroth elements
Aubin Arroyo, Gerardo González Robert
Lüroth series, like regular continued fractions, provide an interesting identification of real numbers with infinite sequences of integers. These sequences give deep arithmetic and…
Generalised Lüroth expansions and a family of Minkowski's Question-Mark functions
Aubin Arroyo
The Minkowski's Question-Mark function is a singular homeomorphism of the unit interval that maps the set of quadratic surds into the rationals. This function has deserved the atte…
On maximally inflected hyperbolic curves
Aubin Arroyo, Erwan Brugallé, Lucia López de Medrano
In this note we study the distribution of real inflection points among the ovals of a real non-singular hyperbolic curve of even degree. Using Hilbert's method we show that for any…
Structure and evolution of strange attractors in non-elastic triangular billiards
Aubin Arroyo, Roberto Markarian, David P. Sanders
We study pinball billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls are non-elastic: the outgoing angle with the normal vector to the…
C^k-Robust transitivity for surfaces with boundary
Aubin Arroyo, Enrique R. Pujals
We prove that C^1-robustly transitive diffeomorphisms on surfaces with boundary do not exist, and we exhibit a class of diffeomorphisms of surfaces with boundary which are C^k-robu…
Bifurcations of periodic and chaotic attractors in pinball billiards with focusing boundaries
Aubin Arroyo, Roberto Markarian, David P. Sanders
We study the dynamics of billiard models with a modified collision rule: the outgoing angle from a collision is a uniform contraction, by a factor lambda, of the incident angle. Th…
Recursive formulas for Welschinger invariants of the projective plane
Aubin Arroyo, Erwan Brugalle, Lucia Lopez de Medrano
Welschinger invariants of the real projective plane can be computed via the enumeration of enriched graphs, called marked floor diagrams. By a purely combinatorial study of these o…