Geodesic
General Approach to Integrating Invertible Dynamical Systems Defined by Transformations from the Cremona group $\operatorname{Cr}(P^n_k)$ of Birational Transformations
Matematičeskie zametki, Tome 68 (2000) no. 5, pp. 699-709

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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. 
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     author = {K. V. Rerikh},
     title = {General {Approach} to {Integrating} {Invertible} {Dynamical} {Systems} {Defined} by {Transformations} from the {Cremona} group $\operatorname{Cr}(P^n_k)$ of {Birational} {Transformations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {699--709},
     publisher = {mathdoc},
     volume = {68},
     number = {5},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2000_68_5_a6/}
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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. Matematičeskie zametki, Tome 68 (2000) no. 5, pp. 699-709. http://geodesic.mathdoc.fr/item/MZM_2000_68_5_a6/