Mathematics (Apr 2020)

On the Exponents of Exponential Dichotomies

  • Flaviano Battelli,
  • Michal Fečkan

DOI
https://doi.org/10.3390/math8040651
Journal volume & issue
Vol. 8, no. 4
p. 651

Abstract

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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.

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