Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Analytic Automorphisms and Transitivity of Analytic Mappings

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

A peer-reviewed article of this Preprint also exists.

Novosad, Z.; Zagorodnyuk, A. Analytic Automorphisms and Transitivity of Analytic Mappings. Mathematics 2020, 8, 2179. Novosad, Z.; Zagorodnyuk, A. Analytic Automorphisms and Transitivity of Analytic Mappings. Mathematics 2020, 8, 2179.

Journal reference: Mathematics 2020, 8, 2179
DOI: 10.3390/math8122179

## Abstract

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.

## Subject Areas

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

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