Geodesic
On invariants and invariant hypersurfaces of complex discrete dynamical systems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2021), pp. 44-55

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First, we introduce the concept of a completely solvable complex real holomorphic system of bigolomorphisms and prove that it forms a multidimensional discrete dynamical system. Then the functional invariants are defined and we find the dimension of the basis of nondegenerate absolute invariants for the class of systems of general position under consideration. Finally, we obtain signs of the limitation of the number of compact invariant hypersurfaces for auxiliary real systems of diffeomorphisms, and on their basis we obtain signs of the limitation of the number of compact invariant hypersurfaces for complex real holomorphic discrete dynamical systems.
Keywords: real holomorphic function of the complex variable, discrete dynamical system, functional invariant
Mots-clés : invariant hypersurface. 
@article{IVM_2021_2_a3,
     author = {V. Yu. Tyshchenko},
     title = {On invariants and invariant hypersurfaces of complex discrete dynamical systems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {44--55},
     publisher = {mathdoc},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_2_a3/}
}
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V. Yu. Tyshchenko. On invariants and invariant hypersurfaces of complex discrete dynamical systems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2021), pp. 44-55. http://geodesic.mathdoc.fr/item/IVM_2021_2_a3/