Abrarov Dmitry. Integrability of the general Euler-poisson equations as the canonical simply connected analytic Liouville-arnold theorem

Natural Sciences / Mathematics / Dynamical systems

Submitted on: Feb 23, 2023, 05:27:51

Description: The Liouville-Arnold integrability of these equations in the analytic smoothness class of the phase flow is revealed. Such analytic integrability is of a functional arithmetic nature and differs sharply from an analogous classical "toroidal" integrability. In particular, the classical Liouville-Arnold theorem in the case of the Euler-Poisson equations is false: "Arnold tori with rectilinear winding dynamics" are not equivariant. Moreover, a constructive equivariant correction of the classical approach by involution of time reversibility leads to the discovery of the phase flow model of the Euler-Poisson equations in the form of the canonical simply connected derivative complex for the simplest meromorphic extension of the simple Lie algebra e_8 which includes, as subcomplexes, the same extensions of the ordered complete list of simple Lie algebras.

The Library of Congress (USA) reference page : http://lccn.loc.gov/cn2013300046.

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