Abstract
This chapter is dedicated to the study of the admissibility theory for exponential dichotomies in continuous time. Again, the arguments build on those in Chapter 2, up to substantial technical complications. To the possible extent, we follow the path of Chapter 3. In particular, we consider both a two-sided and a one-sided dynamics given by an evolution family.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
L. Barreira, C. Valls, Admissibility in the strong and weak senses, Preprint IST, 2017
L. Barreira, D. Dragičević, C. Valls, Strong and weak (L p, L q)-admissibility. Bull. Sci. Math. 138, 721–741 (2014)
L. Barreira, D. Dragičević, C. Valls, Admissibility on the half line for evolution families. J. Anal. Math. 132, 157–176 (2017)
W. Coppel, Dichotomies in Stability Theory. Lecture Notes in Mathematics, vol. 629 (Springer, New York, 1981)
D. Henry, Exponential dichotomies, the shadowing lemma and homoclinic orbits in Banach spaces. Resenhas 1, 381–401 (1994)
Y. Latushkin, T. Randolph, R. Schnaubelt, Exponential dichotomy and mild solutions of nonautonomous equations in Banach spaces. J. Dyn. Differ. Equ. 10, 489–510 (1998)
A. Sasu, Exponential dichotomy for evolution families on the real line. Abstr. Appl. Anal. 2006, 31641, 16 pp. (2006)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Barreira, L., Dragičević, D., Valls, C. (2018). Exponential Dichotomies: Continuous Time. In: Admissibility and Hyperbolicity. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-90110-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-90110-7_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-90109-1
Online ISBN: 978-3-319-90110-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)