Related papers: Complex Arnol'd-Liouville maps
Variational principles play a central role in classical mechanics, providing compact formulations of dynamics and direct access to conserved quantities. While holonomic systems admit well-known action formulations, non-holonomic systems --…
A model of a relativistic particle moving in the Liouville field is investigated. Symmetry group of the system is $SL(2,R)/Z_2$. The corresponding dynamical integrals describe full set of classical trajectories. Dynamical integrals are used…
We describe our recent proposal of a path integral formulation of classical Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics, which concerns the direct coupling of classical and quantum mechanical degrees of…
In this paper we investigate a class of natural Hamiltonian systems with two degrees of freedom. The kinetic energy depends on coordinates but the system is homogeneous. Thanks to this property it admits, in a general case, a particular…
In this article, we discuss some properties of holomorphic fibrations in the complex analytic setting.
- We have suggested using the action-angle variables for the study of a (quasi)particle in quantum ring. We have presented the action-angle variables for three two-dimensional singular oscillator systems - We have suggested a procedure of…
We prove some properties of analytic multiplicative and sub-multiplicative cocycles. The results allow to construct natural invariant analytic sets associated to complex dynamical systems.
The theory of polynomial-like maps is of fundamental importance in holomorphic dynamics. We study dynamical properties of a larger class of maps. Our main result is that, under some natural conditions, a map of this class has a completely…
In this letter, we study the purely nonlinear oscillator by the method of action-angle variables of Hamiltonian systems. The frequency of the non-isochronous system is obtained, which agrees well with the previously known result. Exact…
We consider the one degree-of-freedom Hamiltonian system defined by the Morse potential energy function (the "Morse oscillator"). We use the geometry of the level sets to construct explicit expressions for the trajectories as a function of…
It is shown that, by appropriately defining the eigenfunctions of a function defined on the extended phase space, the Liouville theorem on solutions of the Hamilton--Jacobi equation can be formulated as the problem of finding common…
We study asymptotics of integrals of certain rational functions that depend on parameters in a field $K$ of characteristic zero. We use formal power series to represent the integral and prove certain identities about its coefficients…
In this study we work on a novel Hamiltonian system which is Liouville integrable. In the integrable Hamiltonian model, conserved currents can be represented as Binomial polynomials in which each order corresponds to the integral of motion…
Bi-presymplectic chains of one-forms of arbitrary co-rank are considered. The conditions in which such chains represent some Liouville integrable systems and the conditions in which there exist related bi-Hamiltonian chains of vector fields…
An integrable Hamiltonian system presents monodromy if the action-angle variables cannot be defined globally. As a prototype of classical monodromy with azimuthal symmetry, we consider a linear molecule interacting with external fields and…
The paper studies the complex differentiable functions of double argument and their properties, which are similar to the properties of the holomorphic functions of complex variable: the Cauchy formula, the hyperbolic harmonicity, the…
Just like decent classical difference-difference systems define symplectic maps on suitable phase spaces, their counterparts with properly ordered noncommutative entries come as Heisenberg equations of motion for corresponding quantum…
This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion…
We study dissipative translationally invariant free-fermionic theories with quadratic Liouvillians. Using a Lie-algebraic approach, we solve the Lindblad equation and find the density matrix at all times for arbitrary time dependence of the…
Simplicial complexes are a popular tool used to model higher-order interactions between elements of complex social and biological systems. In this paper, we study some combinatorial aspects of a class of simplicial complexes created by a…