caa a22 4500 475740807 CHVBK 20180406123459.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1023/A:1026619524037 doi (NATIONALLICENCE)springer-10.1023/A:1026619524037 Rerikh K. United Institute for Nuclear Research, Russia aut General Approach to Integrating Invertible Dynamical Systems Defined by Transformations from the Cremona group Cr( P kn) of Birational Transformations [Elektronische Daten] [K. Rerikh] 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. Plenum Publishing Corporation, 2000 dynamical system nationallicence first integrals nationallicence Cremona transformations nationallicence invariant polynomials nationallicence algebraic integrability nationallicence algebraic numbers nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/5-6(2000-11-01), 594-601 0001-4346 68:5-6<594 2000 68 11006 https://doi.org/10.1023/A:1026619524037 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1026619524037 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rerikh K. United Institute for Nuclear Research, Russia aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/5-6(2000-11-01), 594-601 0001-4346 68:5-6<594 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer