Borel summation and splitting of separatrices for the Hénon map
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Publication:5928786
DOI10.5802/aif.1831zbMath0988.37031OpenAlexW1523131750MaRDI QIDQ5928786
Vassili Gelfreich, David Sauzin
Publication date: 4 April 2001
Published in: Annales de l'Institut Fourier (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=AIF_2001__51_2_513_0
Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Invariant manifold theory for dynamical systems (37D10)
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Cites Work
- 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
- Asymptotics beyond all orders and analytic properties of inverse Laplace transforms of solutions
- A refined formula for the separatrix splitting for the standard map
- Splitting of separatrices for standard and semistandard mappings
- Summability of divergent series
- Splitting of a small separatrix loop near the saddle-center bifurcation in area-preserving maps
- Exponentially small splitting of separatrices, matching in the complex plane and Borel summation
- Adiabatic Invariant of the Harmonic Oscillator, Complex Matching and Resurgence
- On the complex separatrices of some standard-like maps
- Exponentially small splittings in Hamiltonian systems
- Exponential asymptotic expansions and approximations of the unstable and stable manifolds of singularly perturbed systems with the Hénon map as an example
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