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On the Exponents of Exponential Dichotomies

Author

Listed:
  • Flaviano Battelli

    (Department of Industrial Engineering and Mathematics, Marche Polytecnic University, 60121 Ancona, Italy)

  • Michal Fečkan

    (Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia
    Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia)

Abstract

An exponential dichotomy is studied for linear differential equations. A constructive method is presented to derive a roughness result for perturbations giving exponents of the dichotomy as well as an estimate of the norm of the difference between the corresponding two dichotomy projections. This roughness result is crucial in developing a Melnikov bifurcation method for either discontinuous or implicit perturbed nonlinear differential equations.

Suggested Citation

  • Flaviano Battelli & Michal Fečkan, 2020. "On the Exponents of Exponential Dichotomies," Mathematics, MDPI, vol. 8(4), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:651-:d:349637
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