Analytic Automorphisms and Transitivity of Analytic Mappings

Zoriana Novosad; Andriy Zagorodnyuk

doi:10.20944/preprints202011.0464.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 16 November 2020 / Approved: 18 November 2020 / Online: 18 November 2020 (10:39:35 CET)

In this paper we investigate analytic automorphisms of complex topological vector spaces and their applications to linear and nonlinear transitive operators. We constructed some examples of polynomial automorphisms which show that a natural analogue of the Jacobian Conjecture for infinite dimensional spaces is not true. Also, we prove that any separable Fréchet space supports a transitive analytic operator which is not a polynomial. We found some connections of analytic automorphisms and algebraic bases of symmetric polynomials and applications to hypercyclisity of composition operators.

topologically transitive operator; hypercyclic operators; function space; analytic functions on Banach spaces; symmetric polynomials on Banach spaces

Computer Science and Mathematics, Analysis

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Analytic Automorphisms and Transitivity of Analytic Mappings

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