Related papers: Partial Reduction and Delaunay/Deprit Variables
Numerous problems in optics, quantum physics, stability analysis, and control of dynamical systems can be brought to an optimization problem with matrix variable subjected to the symplecticity constraint. As this constraint nicely forms a…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
We describe the symplectic reduction construction for the physical phase space in gauge theory and apply it for the BF theory. Symplectic reduction theorem allows us to rewrite the same phase space as a quotient by the gauge group action,…
We investigate quasi-symmetry for small perturbations of the Gidas-Ni-Nirenberg problem involving the $p$-Laplacian and for small perturbations the critical $p$-Laplace equation for $p>2$. To achieve these results, we provide a quantitative…
This paper introduces a new difference scheme to the difference equations for N-body type problems. To find the non-collision periodic solutions and generalized periodic solutions in multi-radial symmetric constraint for the N-body type…
We study deformations of symplectic structures on a smooth manifold $M$ via the quasi-Poisson theory. By a fact, we can deform a given symplectic structure $\omega $ to a new symplectic structure $\omega_t$ parametrized by some element $t$…
The first part of the article is, in fact, the classical Routh method delivered in the language of contemporary theory of Lagrangian systems. But the Routh method deals only with concrete equations and, therefore, can be applied only in the…
This series of papers is devoted to an open-ended project aimed at the solution of Hilbert's sixth problem (concerning joint axiomatization of physics and probability theory) proposed to be constructed in the framework of an all-embracing…
By using an arithmetic fact, we will firstly prove Saari's conjecture in a particular case, which is called the Elliptical Type N-Body Problem, and then we apply it to prove that the variational minimal solution of the planar Newtonian…
Optimization of low-thrust trajectories that involve a larger number of orbit revolutions is considered a challenging problem. This paper describes a high-precision symplectic method and optimization techniques to solve the minimum-energy…
In this paper we prove a kind of rotational symmetry for solutions of semilinear elliptic systems in some bounded cylindrical domains. The symmetry theorems obtained hold for low-Morse index solutions whenever the nonlinearities satisfy…
A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new…
A Theorem due to Guillemin and Sternberg about geometric quantization of Hamiltonian actions of compact Lie groups $G$ on compact Kaehler manifolds says that the dimension of the $G$-invariant subspace is equal to the Riemann-Roch number of…
This paper presents symmetry reduction for material stochastic Lagrangian systems with advected quantities whose configuration space is a Lie group. Such variational principles yield deterministic as well as stochastic constrained…
We study a model of N-component complex fermions with a kinetic term that is second order in derivatives. This symplectic fermion model has an Sp(2N) symmetry, which for any N contains an SO(3) subgroup that can be identified with…
A unitary transformation which relates a many-body quantum mechanics with N=2 Schrodinger supersymmetry to a set of decoupled superparticles is proposed. The simplification in dynamics is achieved at a price of a nonlocal realization of the…
The Suzuki-Trotter decomposition in general allows one to divide the equation of motion of a dynamical system into smaller parts whose integration are easier than the original equation. In this study, we first rewrite by employing feasible…
By carrying out refined point-wise estimates for the mean curvature, we prove better rigidity theorems of Lagrangian and symplectic translating solitons.
We propose the symmetry reduction method of partial differential equations to the system of differential equations with fewer number of independent variables. We also obtain generalized sufficient conditions for the solution found by…
Losev introduced the scheme $X$ of almost commuting elements (i.e., elements commuting upto a rank one element) of $\mathfrak{g}=\mathfrak{sp}(V)$ for a symplectic vector space $V$ and discussed its algebro-geometric properties. We…