51 citations · 311 across the 32 of their papers we have counts for
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On change of slow variables at crossing the separatrices
Anatoly Neishtadt
We consider general (not necessarily Hamiltonian) perturbations of Hamiltonian systems with one degree of freedom near separatrices of the unperturbed system. We present asymptotic…
On phase at a resonance in slow-fast Hamiltonian systems
Yuyang Gao, Anatoly Neishtadt, Alexey Okunev
We consider a slow-fast Hamiltonian system with one fast angular variable (a fast phase) whose frequency vanishes on some surface in the space of slow variables (a resonant surface…
Averaging and passage through resonances in two-frequency systems near separatrices
Anatoly Neishtadt, Alexey Okunev
The averaging method is a classical powerful tool in perturbation theory of dynamical systems. There are two major obstacles to applying the averaging method, resonances and separa…
On the phase change for perturbations of Hamiltonian systems with separatrix crossing
Anatoly Neishtadt, Alexey Okunev
We study the evolution of angular variable (phase) for general (not necessarily Hamiltonian) perturbations of Hamiltonian systems with one degree of freedom near separatrices of th…
On stability of planar solutions of double averaged restricted elliptic three-body problem
Anatoly Neishtadt, Kaicheng Sheng, Vladislav Sidorenko
Double averaged planar restricted elliptic three-body problem has a two-parametric family of stable equilibria. We show that these equilibria are stable in the linear approximation…
Averaging method for systems with separatrix crossing
Anatoly Neishtadt
The averaging method provides a powerful tool for studying evolution in near-integrable systems. Existence of separatrices in the phase space of the underlying integrable system is…