Shilnikov Lemma for a nondegenerate critical manifold of a Hamiltonian system

We prove an analog of Shilnikov Lemma for a normally hyperbolic symplectic critical manifold $M\subset H^{-1}(0)$ of a Hamiltonian system. Using this result, trajectories with small energy $H=\mu>0$ shadowing chains of homoclinic orbits to $M$ are represented as extremals of a discrete variational problem, and their existence is proved. This paper is motivated by applications to the Poincar\'e second species solutions of the 3 body problem with 2 masses small of order $\mu$. As $\mu\to 0$, double collisions of small bodies correspond to a symplectic critical manifold of the regularized Hamiltonian system

Quantum Manifestations of Classical Stochasticity in the Mixed State

We investigate the QMCS in structure of the eigenfunctions, corresponding to mixed type classical dynamics in smooth potential of the surface quadrupole oscillations of a charged liquid drop. Regions of different regimes of classical motion are strictly separated in the configuration space, allowing direct observation of the correlations between the wave function structure and type of the classical motion by comparison of the parts of the eigenfunction, corresponding to different local minima.Comment: 4 pages, 3 figure

Note on cosmographic approach to determining parameters of Barrow entropic dark energy model

The cosmographic approach is used to determine the parameters of the Barrow entropic dark energy model. The model parameters are expressed through the current kinematic characteristics of Universe expansion.Comment: 5 pages , 1 figure, references adde