The AMU meeting will take place on the 19th of December 2024 at 14:30 inthe auditorium number 137 of the faculty of Mathematics and Mechanics of YSU.
Prof. Ashot S Gevorkyan from the Institute for Informatics and Automation Problems, NAS of Armenia, will give a lecture on the topic “ General three-body problem in conformal- Euclidian space: new problems of a low-dimensional dynamical system.”
Abstract:
Despite the huge number of studies of the three-body problem in physics and
mathematics, the study of this problem remains relevant due to both its wide
practical application and taking into account its fundamental importance for the
theory of dynamical systems. In addition, one often has to answer the cognitive
question: is irreversibility fundamental for the description of the classical world?
To answer this question, we considered a reference classical dynamical system, the
general three-body problem, formulating it in conformal Euclidean space and
rigorously proving its equivalence to the Newtonian three-body problem. It has
been proven that a curved configuration space with a local coordinate system
reveals new hidden symmetries of the internal motion of a dynamical system,
which makes it possible to reduce the problem to a sixth-order system instead of
the eighth order. An important consequence of the developed representation is that
the chronologizing parameter of the motion of a system of bodies, which we call
internal time, differs significantly from ordinary time in its properties. In
particular, it more accurately describes the irreversible nature of multichannel
scattering in a three-body system and other chaotic properties of a dynamical
system. The paper derives an equation describing the evolution of the flow of
geodesic trajectories, with the help of which the entropy of the system is
constructed. New criteria for assessing the complexity of a low-dimensional
dynamical system and the dimension of stochastic fractal structures arising in
three-dimensional space are obtained. An effective mathematical algorithm is
developed for the numerical simulation of the general three-body problem, which
is traditionally a difficult-to-solve system of stiff ordinary differential equations.