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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 λ , of the incident angle. These pinball billiards interpolate between a one-dimensional map when λ = 0 and the classical Hamiltonian case of elastic collisions when λ = 1. For all λ < 1, the dynamics is… (More)

- Aubin Arroyo, Roberto Markarian, David P Sanders
- Chaos
- 2012

We study non-elastic billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls of the table are not elastic, as in standard billiards; rather, the outgoing angle of the trajectory with the normal vector to the boundary at the point of collision is a uniform factor λ < 1 smaller than the incoming angle. This leads to… (More)

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 objects, we prove a Caporaso-Harris type formula which allows one to compute Welschinger invariants for configurations of points with any number of complex conjugated points.

- Aubin Arroyo, Isabel Hubard, Klavdija Kutnar, Eugenia O'Reilly Regueiro, Primoz Sparl
- Graphs and Combinatorics
- 2015

- Aubin Arroyo, Erwan Brugallé, Lucia López de Medrano
- Discrete & Computational Geometry
- 2014

We prove that C-robustly transitive diffeomorphisms on surfaces with boundary do not exist, and we exhibit a class of diffeomorphisms of surfaces with boundary which are C−robustly transitive, with k ≥ 2. This class of diffeomorphisms are examples where a version of Palis’ conjecture on surfaces with boundary, about homoclinic tangencies and uniform… (More)

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