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 Mat. Zametki, 2000, Volume 68, Issue 5, Pages 699–709 (Mi mz991)

General Approach to Integrating Invertible Dynamical Systems Defined by Transformations from the Cremona group $\operatorname{Cr}(P^n_k)$ of Birational Transformations

K. V. Rerikh

Joint Institute for Nuclear Research

Abstract: A general approach is developed for integrating an invertible dynamical system defined by the composition of two involutions, i.e., a nonlinear one which is a standard Cremona transformation, and a linear one. By the Noether theorem, the integration of these systems is the foundation for integrating a broad class of Cremona dynamical systems. We obtain a functional equation for invariant homogeneous polynomials and sufficient conditions for the algebraic integrability of the systems under consideration. It is proved that Siegel's linearization theorem is applicable if the eigenvalues of the map at a fixed point are algebraic numbers.

DOI: https://doi.org/10.4213/mzm991

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English version:
Mathematical Notes, 2000, 68:5, 594–601

Bibliographic databases:

UDC: 519
Revised: 27.03.2000

Citation: K. V. Rerikh, “General Approach to Integrating Invertible Dynamical Systems Defined by Transformations from the Cremona group $\operatorname{Cr}(P^n_k)$ of Birational Transformations”, Mat. Zametki, 68:5 (2000), 699–709; Math. Notes, 68:5 (2000), 594–601

Citation in format AMSBIB
\Bibitem{Rer00} \by K.~V.~Rerikh \paper General Approach to Integrating Invertible Dynamical Systems Defined by Transformations from the Cremona group $\operatorname{Cr}(P^n_k)$ of Birational Transformations \jour Mat. Zametki \yr 2000 \vol 68 \issue 5 \pages 699--709 \mathnet{http://mi.mathnet.ru/mz991} \crossref{https://doi.org/10.4213/mzm991} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1835452} \zmath{https://zbmath.org/?q=an:1060.14508} \elib{http://elibrary.ru/item.asp?id=13947548} \transl \jour Math. Notes \yr 2000 \vol 68 \issue 5 \pages 594--601 \crossref{https://doi.org/10.1023/A:1026619524037} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000166684000007} 

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• https://doi.org/10.4213/mzm991
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