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On Some Characterizations for Uniform Dichotomy of Evolution Operators in Banach Spaces

Author

Listed:
  • Rovana Boruga (Toma)

    (Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, 300223 Timişoara, Romania
    These authors contributed equally to this work.)

  • Mihail Megan

    (Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, 300223 Timişoara, Romania
    Academy of Romanian Scientists, 050094 Bucharest, Romania
    These authors contributed equally to this work.)

Abstract

The present paper deals with two of the most significant behaviors in the theory of dynamical systems: the uniform exponential dichotomy and the uniform polynomial dichotomy for evolution operators in Banach spaces. Assuming that the evolution operator has uniform exponential growth, respectively uniform polynomial growth, we give some characterizations for the uniform exponential dichotomy, respectively for the uniform polynomial dichotomy. The proof techniques that we use for the polynomial case are new. In addition, connections between the concepts approached are established.

Suggested Citation

  • Rovana Boruga (Toma) & Mihail Megan, 2022. "On Some Characterizations for Uniform Dichotomy of Evolution Operators in Banach Spaces," Mathematics, MDPI, vol. 10(19), pages 1-21, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3704-:d:937847
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