Exponentially small separatrix splittings and almost invisible homoclinic bifurcations in some billiard tables
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Publication:2572284
DOI10.1016/j.physd.2005.07.012zbMath1152.37336OpenAlexW2010835490MaRDI QIDQ2572284
Publication date: 16 November 2005
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.physd.2005.07.012
Numerical experimentsBilliardsExponentially small phenomenaHomoclinic bifurcationsSeparatrix splitting
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Related Items (4)
Stability of the phase motion in race-track microtrons ⋮ Splitting of separatrices, scattering maps, and energy growth for a billiard inside a time-dependent symmetric domain close to an ellipse ⋮ Exponentially Small Asymptotic Formulas for the Length Spectrum in Some Billiard Tables ⋮ Break-up of resonant invariant curves in billiards and dual billiards associated to perturbed circular tables
Uses Software
Cites Work
- Splitting of separatrices for the Chirikov standard map
- Transport in Hamiltonian systems
- On separatrix splitting of some quadratic area-preserving maps of the plane
- A proof of the exponentially small transversality of the separatrices for the standard map
- A refined formula for the separatrix splitting for the standard map
- Exponentially small splitting of separatrices for perturbed integrable standard-like maps
- Homoclinic billiard orbits inside symmetrically perturbed ellipsoids
- Singular Separatrix Splitting and the Melnikov Method: An Experimental Study
- Poincaré - Melnikov - Arnold method for analytic planar maps
- Separatrices splitting for Birkhoff’s billiard in symmetric convex domain, closed to an ellipse
- Splitting of separatrices: perturbation theory and exponential smallness
- Borel summation and splitting of separatrices for the Hénon map
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