Abstract
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) \( {D}_p^n \) 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.
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Translated from Kibernetika i Sistemnyi Analiz, No. 3, May–June, 2019, pp. 45–55.
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Kharchenko, V.P., Glazunov, N.M. Formal and Non-Archimedean Structures of Dynamic Systems on Manifolds. Cybern Syst Anal 55, 384–392 (2019). https://doi.org/10.1007/s10559-019-00145-4
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DOI: https://doi.org/10.1007/s10559-019-00145-4