Exponentially Small Asymptotic Formulas for the Length Spectrum in Some Billiard Tables
From MaRDI portal
Publication:5739440
DOI10.1080/10586458.2015.1076361zbMath1360.37093arXiv1504.08243OpenAlexW1566891079MaRDI QIDQ5739440
Anna Tamarit-Sariol, Rafael Ramírez-Ros, Pau Martín
Publication date: 15 July 2016
Published in: Experimental Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1504.08243
Simulation of dynamical systems (37M05) Convex sets in (2) dimensions (including convex curves) (52A10) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)
Related Items
On the length and area spectrum of analytic convex domains ⋮ On the asymptotic wavenumber of spiral waves in $\lambda -\omega $ systems
Cites Work
- Unnamed Item
- Unnamed Item
- Computing Mather's \(\beta\)-function for Birkhoff billiards
- Exponentially small splitting for the pendulum: A classical problem revisited
- Resurgence of inner solutions for perturbations of the McMillan map
- Exponentially small splitting of separatrices in the perturbed McMillan map
- Transport in Hamiltonian systems
- A criterion for the non-existence of invariant circles
- Spectral invariants of convex planar regions
- An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum
- The propagation of singularities along gliding rays
- A proof of the exponentially small transversality of the separatrices for the standard map
- Exponentially small splitting of separatrices for perturbed integrable standard-like maps
- The principle of least action in geometry and dynamics
- Break-up of resonant invariant curves in billiards and dual billiards associated to perturbed circular tables
- Exponentially small separatrix splittings and almost invisible homoclinic bifurcations in some billiard tables
- The billiard ball problem on a table with a convex boundary - An illustrative dynamical problem. I. The invariant integral
- Estimation of the Amplitude of Resonance in the General Standard Map
- Non-persistence of resonant caustics in perturbed elliptic billiards
- Exponentially and non-exponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation
- The Frequency Map for Billiards inside Ellipsoids
- Symplectic maps, variational principles, and transport
- Elliptical billiards and Poncelet’s theorem
- Greene's residue criterion
- Singular Separatrix Splitting and the Melnikov Method: An Experimental Study
- Poincaré - Melnikov - Arnold method for analytic planar maps
- Exponentially small splittings in Hamiltonian systems
- KAM Theory and a Partial Justification of Greene's Criterion for Nontwist Maps
- Splitting of separatrices: perturbation theory and exponential smallness
- The Inner Equation for Generalized Standard Maps
- Can One Hear the Shape of a Drum?
- Borel summation and splitting of separatrices for the Hénon map
