Related papers: A Short Comparison of Classical Complex Dynamics a…
This is a survey article on classical groups (over arbitrary division rings) and their geometries.
A general dynamical system composed by two coupled sectors is considered. The initial time configuration of one of these sectors is described by a set of classical data while the other is described by standard quantum data. These dynamical…
Building on a model recently proposed by F. Calogero, we postulate the existence of a coherent, long--range universal tremor affecting any stable and confined classical dynamical system. Deriving the characteristic fluctuative unit of…
We introduce semiframes (an algebraic structure) and investigate their duality with semitopologies (a topological one). Both semitopologies and semiframes are relatively recent developments, arising from a novel application of topological…
In one dimension, the theory of the $G$-normal distribution is well-developed, and many results from the classical setting have a nonlinear counterpart. Significant challenges remain in multiple dimensions, and some of what has already been…
The long-standing challenge to describing charged particle dynamics in strong classical electromagnetic fields is how to incorporate classical radiation, classical radiation reaction and quantized photon emission into a consistent unified…
I shortly describe semi-classical models of spinning electron and list a number of theoretical issues where these models turn out to be useful, see arXiv:1710.07135 for details. Then I discuss the possibility to extend the range of…
We investigate the random dynamics of rational maps on the Riemann sphere and the dynamics of semigroups of rational maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, in most cases, the chaos of the…
The dynamics of systems composed of a classical sector plus a quantum sector is studied. We show that, even in the simplest cases, (i) the existence of a consistent canonical description for such mixed systems is incompatible with very…
Within the frames of the analytical mechanics the method of the description of dynamics of nonequilibrium systems of potentially interacting elements is develops. The method is based on an opportunity of representation of nonequilibrium…
This paper studies first the differential inequalities that make it possible to build a global theory of pseudo-holomorphic functions in the case of one or several complex variables. In the case of one complex dimension, we prove that the…
The main directions in the development of the nonholonomic dynamics are briefly considered in this paper. The first direction is connected with the general formalizm of the equations of dynamics that differs from the Lagrangian and…
This work is devoted to review the modern geometric description of the Lagrangian and Hamiltonian formalisms of the Hamilton--Jacobi theory. The relation with the "classical" Hamiltonian approach using canonical transformations is also…
The nongeneric six- and eightdimensional orbits of SO(4,2) are described in explicitly covariant way. The relevant Hamiltonian dynamical systems are constructed and canonically quantized. It is shown that the resulting unitary…
In this manuscript we systematically review known results of local dynamics of discrete local holomorphic dynamics near fixed points in one and several complex variables as well as the consequences in global dynamics.
Statistical physics has proven to be a very fruitful framework to describe phenomena outside the realm of traditional physics. The last years have witnessed the attempt by physicists to study collective phenomena emerging from the…
We consider quantitative convergence analysis for hypocoercive dynamics such as Langevin and Lindblad equations describing classical and quantum open systems. Our goal is to provide an overview of recent results of hypocoercivity estimates…
The analogy between monodromy in dynamical (Hamiltonian) systems and defects in crystal lattices is used in order to formulate some general conjectures about possible types of qualitative features of quantum systems which can be interpreted…
We investigate the possibility that the semiclassical limit of quantum mechanics might be correctly described by a classical dynamical theory, other than standard classical mechanics. Using a set of classicality criteria proposed in a…
Recent developments in Macroscopic Fluctuation Theory show that many interacting particle systems behave macroscopically as a combination of a gradient flow with Hamiltonian dynamics. This observation leads to the natural question how these…