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Analytic Automorphisms and Transitivity of Analytic Mappings

Author

Listed:
  • 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)

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.

Suggested Citation

  • Zoriana Novosad & Andriy Zagorodnyuk, 2020. "Analytic Automorphisms and Transitivity of Analytic Mappings," Mathematics, MDPI, vol. 8(12), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2179-:d:457828
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