Regular and Chaotic Dynamics
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Erratum to: On Some Invariants of Birkhoff Billiards Under Conjugacy
Regular and Chaotic Dynamics - Tập 27 - Trang 757-757 - 2022
Chaos in Bohmian Quantum Mechanics: A Short Review
Regular and Chaotic Dynamics - - 2020
This is a short review of the theory of chaos in Bohmian quantum
mechanics based on our series of works in this field.
Our first result is the development of a generic theoretical mechanism
responsible for the generation of chaos in an
arbitrary Bohmian system (in 2 and 3 dimensions). This mechanism
allows us to explore the effect of chaos on Bohmian trajectories
and study in detail (both analytic...... hiện toàn bộ
Invariant manifolds at infinity of the RTBP and the boundaries of bounded motion
Regular and Chaotic Dynamics - Tập 19 - Trang 745-765 - 2014
Invariant manifolds of a periodic orbit at infinity in the planar circular RTBP are studied. To this end we consider the intersection of the manifolds with the passage through the barycentric pericenter. The intersections of the stable and unstable manifolds have a common even part, which can be seen as a displaced version of the two-body problem, and an odd part which gives rise to a splitting. T...... hiện toàn bộ
On Phase at a Resonance in Slow-Fast Hamiltonian Systems
Regular and Chaotic Dynamics - Tập 28 Số 4-5 - Trang 585-612 - 2023
Stability of the Relative Equilibria in the Two-body Problem on the Sphere
Regular and Chaotic Dynamics - Tập 26 - Trang 402-438 - 2021
We consider the 2-body problem in the sphere
$$\mathbb{S}^{2}$$
. This problem is modeled by a Hamiltonian system with
$$4$$
degrees of freedom and, following the approach given in [4], allows us to reduce the study to a system of ...... hiện toàn bộ
Transformation of a pair of commuting Hamiltonians quadratic in momenta to canonical form and real partial separation of variables for the Clebsch top
Regular and Chaotic Dynamics - Tập 15 - Trang 652-658 - 2010
In the case of two degrees of freedom the simultaneous diagonalization of pairs of Hamiltonians quadratic on momenta that commute with respect to the standard Poisson bracket is considered. A general scheme of partial separation of variables for such pairs is discussed. As an example the Clebsch top is considered.
Elliptic Fixed Points with an Invariant Foliation: Some Facts and More Questions
Regular and Chaotic Dynamics - Tập 27 Số 1 - Trang 43-64 - 2022
On constructing simple examples of three-dimensional flows with multiple heteroclinic cycles
Regular and Chaotic Dynamics - Tập 20 - Trang 679-690 - 2015
In this work we suggest a simple method for constructing G-equivariant systems of ODEs in ℝ3 (i.e., systems whose trajectories are invariant under the action of this group on ℝ3) that possess multiple disjoint heteroclinic networks. Heteroclinic networks under consideration consist of saddle equilibria that belong to coordinate axes and one-dimensional separatrices connecting them. We require thes...... hiện toàn bộ
Embedding the Kepler Problem as a Surface of Revolution
Regular and Chaotic Dynamics - Tập 23 - Trang 695-703 - 2018
Solutions of the planar Kepler problem with fixed energy h determine geodesics of the corresponding Jacobi–Maupertuis metric. This is a Riemannian metric on ℝ2 if h ⩾ 0 or on a disk D ⊂ ℝ2 if h < 0. The metric is singular at the origin (the collision singularity) and also on the boundary of the disk when h < 0. The Kepler problem and the corresponding metric are invariant under rotations of the p...... hiện toàn bộ
Normal form of a quantum Hamiltonian with one and a half degrees of freedom near a hyperbolic fixed point
Regular and Chaotic Dynamics - Tập 13 - Trang 377-402 - 2008
According to classical result of Moser [1] a real-analytic Hamiltonian with one and a half degrees of freedom near a hyperbolic fixed point can be reduced to the normal form by a real-analytic symplectic change of variables. In this paper the result is extended to the case of the non-commutative algebra of quantum observables.We use an algebraic approach in quantum mechanics presented in [2] and d...... hiện toàn bộ
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