Annals of Functional Analysis

Stability of the Lyapunov exponents under perturbations

Luis Barreira and Claudia Valls

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Abstract

For a linear-delay equation on an arbitrary Banach space, we describe a condition so that the Lyapunov exponents of the equation persist under sufficiently small linear as well as nonlinear perturbations. We consider both cases of discrete and continuous time with the study of delay-difference equations and delay equations, respectively. The delay can be any number from zero to infinity.

Article information

Source
Ann. Funct. Anal., Volume 8, Number 3 (2017), 398-410.

Dates
Received: 11 July 2016
Accepted: 13 November 2016
First available in Project Euclid: 16 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.afa/1494900338

Digital Object Identifier
doi:10.1215/20088752-2017-0005

Mathematical Reviews number (MathSciNet)
MR3690002

Zentralblatt MATH identifier
1379.34063

Subjects
Primary: 34D08: Characteristic and Lyapunov exponents
Secondary: 34K20: Stability theory

Keywords
delay equations Lyapunov exponents perturbations

Citation

Barreira, Luis; Valls, Claudia. Stability of the Lyapunov exponents under perturbations. Ann. Funct. Anal. 8 (2017), no. 3, 398--410. doi:10.1215/20088752-2017-0005. https://projecteuclid.org/euclid.afa/1494900338


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References

  • [1] L. Barreira and Y. Pesin, Nonuniform Hyperbolicity, Encyclopedia Math. Appl. 115, Cambridge Univ. Press, Cambridge, 2007.
  • [2] L. Barreira and C. Valls, Stability of nonautonomous differential equations in Hilbert spaces, J. Differential Equations 217 (2005), no. 1, 204–248.
  • [3] L. Barreira and C. Valls, Nonautonomous difference equations and a Perron-type theorem, Bull. Sci. Math. 136 (2012), no. 3, 277–290.
  • [4] L. Barreira and C. Valls, A Perron-type theorem for nonautonomous delay equations, Cent. Eur. J. Math. 11 (2013), no. 7, 1283–1295.
  • [5] A. Czornik and A. Nawrat, On the perturbations preserving spectrum of discrete linear systems, J. Difference Equ. Appl. 17 (2011), no. 1–2, 57–67.
  • [6] J. Hale, Dynamical systems and stability, J. Math. Anal. Appl. 26 (1969), 39–59.
  • [7] J. Hale and S. Verduyn Lunel, Introduction to Functional-Differential Equations, Appl. Math. Sci. 99, Springer, New York, 1993.
  • [8] Y. Hino, S. Murakami, and T. Naito, Functional-Differential Equations with Infinite Delay, Lecture Notes in Math. 1473, Springer, Berlin, 1991.
  • [9] J. Kato, Stability problem in functional differential equations with infinite delay, Funkcial. Ekvac. 21 (1978), no. 1, 63–80.
  • [10] R. Mañé, “Lyapunov exponents and stable manifolds for compact transformations” in Geometric Dynamics (Rio de Janeiro, 1981), Lecture Notes in Math. 1007, Springer, Berlin, 1983, 522–577.
  • [11] K. Matsui, H. Matsunaga, and S. Murakami, Perron type theorem for functional differential equations with infinite delay in a Banach space, Nonlinear Anal. 69 (2008), no. 11, 3821–3837.
  • [12] H. Matsunaga and S. Murakami, Some invariant manifolds for functional difference equations with infinite delay, J. Difference Equ. Appl. 10 (2004), no. 7, 661–689.
  • [13] M. Pituk, Asymptotic behavior and oscillation of functional differential equations, J. Math. Anal. Appl. 322 (2006), no. 2, 1140–1158.
  • [14] M. Pituk, A Perron type theorem for functional differential equations, J. Math. Anal. Appl. 316 (2006), no. 1, 24–41.
  • [15] D. Ruelle, Characteristic exponents and invariant manifolds in Hilbert space, Ann. of Math. (2) 115 (1982), no. 2, 243–290.