On the splitting of invariant manifolds in multidimensional near-integrable Hamiltonian systems

By P. Lochak, Jean-Pierre Marco, D. Sauzin. 2003

103 citations recorded by the source corpus.

Subfields: Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d72abaf27e7b5d81a6d13fe8ce28c2b82cfeb8c0

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In Statistical and Nonlinear Physics

1. R. Llave
2. Marcel Guardia
3. Pau Martín
4. Tere M. Seara
5. Ernest Fontich
6. Amadeu Delshams
7. Inmaculada Baldomá

Citations in the corpus

• Exponentially small splitting of separatrices beyond Melnikov analysis: rigorous results (2012, methodology): “The method in [58,45] uses the fact that, in the considered systems, the manifolds can be written as graphs of the gradient of generating functions in suitable domains.”
• Oscillatory motions for the restricted planar circular three body problem (2012, methodology): “435 To study the distance between the invariant manifolds of infinity, we follow the approach proposed in [22,33].”
• GEOMETRIC PROPERTIES OF THE SCATTERING MAP OF A NORMALLY HYPERBOLIC INVARIANT MANIFOLD (2008, methodology): “Notably, these formulas are very similar to the geometric formulas for the convergent Melnikov functions [23,24,28,46,59,66], and for the other quantities appearing in variational calculus [48].”