Titlebook: Spectra and Normal Forms; Luís Barreira,Claudia Valls Book 2024 The Editor(s) (if applicable) and The Author(s), under exclusive license t

丛林

Spectra and Examples,ossible forms of the tempered spectrum and we give explicit examples of all of them. More precisely, for each possible form we describe explicitly a sequence of invertible matrices with that tempered spectrum.

火车车轮

Asymptotic Behavior,nonlinear. It turns out that all Lyapunov exponents of the perturbed dynamics still belong to some connected component of the tempered spectrum of the linear dynamics. This result depends strongly on the use of Lyapunov norms, which are also used in other parts of the book.

voluble

ESPY

LIEN

Asymptotic Behavior,pered spectrum. We also consider the asymptotic behavior of a linear dynamics under exponentially decaying perturbations that can either be linear or nonlinear. It turns out that all Lyapunov exponents of the perturbed dynamics still belong to some connected component of the tempered spectrum of the

Femine

congenial

Parameter-Dependent Dynamics,rbation of a linear dynamics and we describe how the tempered spectrum may vary. Then we study the smooth dependence of a normal form on a parameter when the nonlinear perturbation depends smoothly on the parameter.

SOB

牙齿

Infinite-Dimensional Dynamics,s the description of all possible forms of the tempered spectrum for a sequence of compact linear operators, which leads to new forms of the spectrum. We also consider the construction of normal forms. Finally, we give examples of sequences of compact linear operators for all possible forms of the t

RACE

Stable and Unstable Foliations,n of a tempered exponential dichotomy. One can also construct a stable foliation, simply by reversing time and so the corresponding details are omitted. The two foliations are crucial for the construction of smooth conjugacies in Chapter 8.