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Analytic Automorphisms and Transitivity of Analytic Mappings
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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.
Title: Analytic Automorphisms and Transitivity of Analytic Mappings
Description:
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.
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