Transversal intersection of separatrices and branching of solutions as obstructions to the existence of an analitic integral in many-dimensional system. I. Basic results: Separatrices of hyperbolic periodic points.

Título inglés	Transversal intersection of separatrices and branching of solutions as obstructions to the existence of an analitic integral in many-dimensional system. I. Basic results: Separatrices of hyperbolic periodic points.
Título español	Intersección transversal de separatrices y ramificaciones de resoluciones como obstrucciones a la existencia de una integral analítica en sistemas multidimensionales. I. Resultado básico. Separatrices de puntos periódicos hiperbólicos.
Autor/es	Dovbysh, Sergei A.
Organización	Inst. Mech. Moscow State Univ., Moscú, Rusia
Revista	0010-0757
Publicación	1999, 50 (2): 119-197, 49 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	It is well-known that the existence of transversally intersecting separatrices of hyperbolic periodic solutions leads, in a typical situation, to complicated and irregular dynamics. Therefore, in the case of a two-dimensional mapping or a three-dimensional flow, with this transversality property, there is no non-trivial analytic or meromorphic first integral, i.e., a function constant along each trajectory of the system under consideration. Additional robust conditions are obtained and discussed that guarantee the absence of such an integral in the many-dimensional case, regardless of the finite dimension in question (the strongest analytic non-integrability). These conditions guarantee also the absence of any non-trivial analytic one-parameter symmetry group, and, more generally, analytic or meromorphic vector fields generating a local symmetry, i.e., a local phase flow commuting with the system under consideration. Furthermore, the analytic centralizer of the system is discrete in the compact-open topology. A differential-topological structure of the invariant set of quasi-random motions is studied for this purpose. The approach used is essentially geometrical. Some related topics are also discussed.
Clasificación UNESCO	121003
Palabras clave español	Dinámica topológica ; Funciones analíticas ; Análisis multivariante ; Problemas hiperbólicos
Código MathReviews	MR1706235
Código Z-Math	Zbl 0945.37014
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