Analytic Automorphisms and Transitivity of Analytic Mappings

Zoriana Novosad and Andriy Zagorodnyuk
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Zoriana Novosad: Department of Higher Mathematics and Quantitative Methods 10, Lviv University of Trade and Economics, Tuhan-Baranovsky Street, 79005 Lviv, Ukraine
Andriy Zagorodnyuk: Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenka Street, 76018 Ivano-Frankivsk, Ukraine

Mathematics, 2020, vol. 8, issue 12, 1-13

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 that 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 that is not a polynomial. We found some connections of analytic automorphisms and algebraic bases of symmetric polynomials and applications to hypercyclicity of composition operators.

Keywords: topologically transitive operator; hypercyclic operators; function space; analytic functions on Banach spaces; symmetric polynomials on Banach spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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