Workshop on Recent Developments in Symplectic Dynamics
Title Kupka-Smale Genericity in Analytic Convex Billiards
In this work we prove that the analytic strongly convex billiards satisfying the Kupka-Smale conditions are generic in the usual analytic topology. As a result, generic convex analytic billiards are maximal chaotic in the sense that for every rational rotation number, $p/q$, there exists at least a $(p,q)$-periodic orbit having all its homoclinic intersections being transverse. In addition, when restricting to the Aubrey-Mather sets, we deduce that, generically, for every rational rotation number, the associated Aubrey-Mather set is uniformly hyperbolic.
This is a joint work with A. Florio, M. Leguil, T.M-Seara
Date & Time
November 04, 2026 | 4:00pm – 5:00pm
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11/04/2026 16:00
11/04/2026 17:00
Workshop on Recent Developments in Symplectic Dynamics
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Topic: Title Kupka-Smale Genericity in Analytic Convex Billiards
Speakers: Inmaculada Concepcion Baldomá Barraca, Institute for Advanced Study
More: https://www.ias.edu/math/events/workshop-recent-developments-symplectic-dynamics-12
In this work we prove that the analytic strongly convex billiards
satisfying the Kupka-Smale conditions are generic in the usual
analytic topology. As a result, generic convex analytic billiards are
maximal chaotic in the sense that for every rational rotation number,
$p/q$, there exists at least a $(p,q)$-periodic orbit having all its
homoclinic intersections being transverse. In addition, when
restricting to the Aubrey-Mather sets, we deduce that, generically,
for every rational rotation number, the associated Aubrey-Mather set
is uniformly hyperbolic.
This is a joint work with A. Florio, M. Leguil, T.M-Seara
Simonyi Hall 101
a7a99c3d46944b65a08073518d638c23
Location
Simonyi Hall 101Speakers
Inmaculada Concepcion Baldomá Barraca, Institute for Advanced Study