# Abrarov Dmitry. A Galois-theory Scheme Of The Euler-poisson Equations And Its Pendulum Interpretation In The Canonical Lobachevsky Function Space (answering P. Deligne questions)

## Natural Sciences / Mathematics / Dynamical systems

Submitted on: Jul 03, 2022, 00:44:51

Description: In accordance with the central result of the monograph  and its complementary argumentation in âE", the Euler-Poisson equations have an exact analytic general solution. Below we describe the corresponding scheme of the equivariant Galois theory for these equations, which directly gives an explicit analytical form of the general and particular solutions of the original equations, associated with L-functions of E/Q curves. These solutions represent the spectrum of the Hamiltonian of the canonical four-dimensional conical pendulum, which has the meaning of the canonical analytic pendulum (q-pendulum, see ). Such a pendulum is a classical mathematical pendulum with the condition of time reversibility invariance of its phase flow, induced by a similar condition for the Euler-Poisson equations. The phase flow of this pendulum has an isometry realization of the canonical Lobachevsky function space, which is represented by a canonical simply connected meromorphic extension of the classical three-dimensional Lobachevsky space. The analytic realization of the equivariant Galois theory is the property of bimodular parametrization of elliptic curves with rational coefficients. This parametrization represents the canonical loxodromic isometry of a three-dimensional sphere, locally described by the Kowalewskaya differential equations, which are the canonical normal form of the Euler-Poisson equations. The symmetry of this model has a simply connected meromorphic Galois structure; in particular, its periods are interpreted as solutions of the Fermat and Beal Diophantine equations. The geometric realization of the equivariant Galois theory is the derived self-duality of the canonical function Lobachevsky space (or, equivalently, is the derived self-duality of the great circles geodesic flow on a four-sphere based on the meromorphic algebra e_8 (Q(s)), see ), canonically coordinated by the functional equation for the function I¶(s,I"_12 (q)), and its dynamic r...

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