Формальные и неархимедовы структуры динамических систем на многообразиях / Харченко В. П., Глазунов Н. М. (2019)
Ukrainian

English  Cybernetics and Systems Analysis   /     Issue (2019, 55 (3))

Kharchenko V.P., Glazunov N.M.
Formal and nonarchimedian structures of dynamic systems on manifolds

New results are presented and a brief review is given for new methods of the theory of dynamic systems on manifolds over local fields and formal groups over local rings. For the analysis of n-dimensional manifolds and dynamic systems on such manifolds, formal structures are used, in particular, n-dimensional formal groups. Infinitesimal deformations are presented in terms of formal groups. The well-known one-dimensional case is extended and n-dimensional (n ≥ 1) analytic mappings of an open p-adic polydisc (n-disk) Dpn are considered. The n-dimensional analogs of modules arising in formal and non-Archimedean dynamic systems are introduced and investigated and their formal-algebraic structure is presented. Rigid structures, objects, and methods are outlined. From the point of view of systems analysis, new, namely formal and non-Archimedean, faces and structures of systems, mappings and iterations of mappings between these faces and structures are introduced and investigated. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: commutative formal group scheme, deformation, dynamic system, formal group, formal module, local ring, module of differentials, Deformation, Dynamical systems, Group theory, Mapping, Systems analysis, formal group, formal module, Group schemes, Local ring, module of differentials, Rigid structures


Cite:
Kharchenko V.P., Glazunov N.M. (2019). Formal and nonarchimedian structures of dynamic systems on manifolds. Cybernetics and Systems Analysis, 55 (3), 45-55. doi: https://doi.org/10.1007/s10559-019-00145-4 http://jnas.nbuv.gov.ua/article/UJRN-0000986316 [In Russian].


 

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