Displaying similar documents to “Absorbers: Definitions, properties and applications.”

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.

Sergei A. Dovbysh (1999)

Collectanea Mathematica

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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...

The Abel equation and total solvability of linear functional equations

G. Belitskii, Yu. Lyubich (1998)

Studia Mathematica

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We investigate the solvability in continuous functions of the Abel equation φ(Fx) - φ(x) = 1 where F is a given continuous mapping of a topological space X. This property depends on the dynamics generated by F. The solvability of all linear equations P(x)ψ(Fx) + Q(x)ψ(x) = γ(x) follows from solvability of the Abel equation in case F is a homeomorphism. If F is noninvertible but X is locally compact then such a total solvability is determined by the same property of the cohomological...

On topological classification of complex mappings

Hadi Seyedinejad, Ali Zaghian (2015)

Annales Polonici Mathematici

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We study the topological invariant ϕ of Kwieciński and Tworzewski, particularly beyond the case of mappings with smooth targets. We derive a lower bound for ϕ of a general mapping, which is similarly effective as the upper bound given by Kwieciński and Tworzewski. Some classes of mappings are identified for which the exact value of ϕ can be computed. Also, we prove that the variation of ϕ on the source space of a mapping with a smooth target is semicontinuous in the Zariski topology. ...