Absorbers: Definitions, properties and applications.
The Abel equation and total solvability of linear functional equations
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 equation φ(Fx)...
Functional equations in real-analytic functions
The equation φ (x) = g(x,φ (x)) in spaces of real-analytic functions is considered. Connections between local and global aspects of its solvability are discussed.
The real-analytic solutions of the Abel functional equation
For the Abel equation on a real-analytic manifold a dynamical criterion of solvability in real-analytic functions is proved.
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