caa a22 4500 445835850 CHVBK 20180317145330.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00209-010-0665-x doi (NATIONALLICENCE)springer-10.1007/s00209-010-0665-x Lyapunov functions versus exponential contractions [Elektronische Daten] [Luis Barreira, Claudia Valls] For nonautonomous linear equations in a Banach space admitting a nonuniform version of exponential contraction, we give an optimal characterization of the exponential behavior in terms of strict Lyapunov sequences. In particular, we construct explicitly strict Lyapunov sequences for each exponential contraction. We also consider the particular case of quadratic Lyapunov functions, and we use the corresponding characterization of the exponential behavior in terms of these functions to show that the stability of an exponential contraction persists under sufficiently small perturbations. Springer-Verlag, 2010 Lyapunov functions nationallicence Exponential contractions nationallicence Barreira Luis Departamento de Matemática, Instituto Superior Técnico, 1049-001, Lisbon, Portugal aut Valls Claudia Departamento de Matemática, Instituto Superior Técnico, 1049-001, Lisbon, Portugal aut Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 187-196 0025-5874 268:1-2<187 2011 268 209 https://doi.org/10.1007/s00209-010-0665-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0665-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Barreira Luis Departamento de Matemática, Instituto Superior Técnico, 1049-001, Lisbon, Portugal aut NATIONALLICENCE 700 1- Valls Claudia Departamento de Matemática, Instituto Superior Técnico, 1049-001, Lisbon, Portugal aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 187-196 0025-5874 268:1-2<187 2011 268 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer