# Abrarov Dmitry. General Solution Of The Euler-poisson Equations As A Canonical Functional Exponent Associated With The Riemann Zeta-function In Real-time Context

## Natural Sciences / Mathematics / Dynamical systems

Submitted on: Apr 26, 2022, 19:01:55

Description: The Euler-Poisson second-order differential equations describing the analytic dynamics of tops determine the canonical functional exponent exp I¶(s,I"_12 (q)) as the canonical functional analogue of the classical exponent. This is a key mathematical aspect of the canonical solvability of the Euler-Poisson equations. This exponent is a canonical analytic generalized function (). It has a hidden autorecursive 3d-vector-valued structure and is the general solution of these dynamic equations, which the normal form is already the first order differential supersymmetric Kowalewskaya equations. The classics skips this general solution neglecting of the functional symmetry of the time reversibility of the Hamiltonian of the original equations. The Euler-Poisson equations have a hidden functional and supersymmetric Galois structure induced by this formally simple, but, in fact, fundamental symmetry (autorecursively symmetrizing the signs of the classical solutions-theta-quadratures). The Euler-Poisson equations are solvable equations in the canonical sense of the canonical functional analogue of the classical Galois theory. The function exp I¶(s,I"_12 (q)) represents the potential of the â„‚-analytic flow of great circles on the 3d-sphere, as well as, the potential of self-conjugation in the space of functional quaternions and the potential of the ball gravitational dipole (). The L-function I¶(s,I"_12 (q)) represents the general solution of the differential kinematic Poisson equations and the conjugation potential in the space of functional quaternions. The phase flow of the Euler-Poisson equations is an SO(3)-realization of the canonical functional exponent; it has the structure of a canonical mapping of the central symmetry of the 3d-sphere, which is equivalent to the self-conjugation of analytic time (hypothetical real time). Conjectures concerning the dynamical role of the Riemann zeta function I¶(s) are formulated: the exponent of I¶(s) (âEśdynamic I¶(s)âEť) ...

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