Spectral Theory of Nonautonomous Differential Equations

Thai Son Doan
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Thai Son Doan: Vietnam Academy of Science and Technology, Institute of Mathematics

Chapter Chapter 1 in Spectral Theory of Nonautonomous Dynamical Systems and Applications, 2024, pp 1-22 from Springer

Abstract: Abstract The central aim in this chapter is to develop a spectral theory for linear nonautonomous differential equations of the form x ̇ ( t ) = A ( t ) x . $$\displaystyle \dot x(t)=A(t)x. $$ In Sect. 1.1, we recall two well-developed spectral theories, namely, Lyapunov spectrum and Sacker-Sell spectra, for nonautonomous differential equations on the half real line ( I = ℝ 0 + $$I=\mathbb {R}_{0}^{+}$$ ) and on the whole real line ( I = ℝ $$I=\mathbb {R}$$ ). Section 1.2 is devoted to developing a Bohl spectral theory for nonautonomous differential equations. The content of this section is a part of Doan et al. (J Dyn Differ Equ 29(4):1459–1485, 2017).

Date: 2024
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DOI: 10.1007/978-981-97-5520-2_1

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