On a Floquet theory for almost-periodic, two-dimensional linear systems
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This article is published in Journal of Differential Equations.The article was published on 1980-08-01 and is currently open access. It has received 77 citations till now. The article focuses on the topics: Floquet theory & Linear system.read more
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Random Dynamical Systems
TL;DR: This chapter establishes the framework of random dynamical systems and introduces the concept of random attractors to analyze models with stochasticity or randomness.
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Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2.
Book
Nonuniform Hyperbolicity: Dynamics of Systems with Nonzero Lyapunov Exponents
Luis Barreira,Yakov Pesin +1 more
TL;DR: In this paper, the authors present a self-contained and comprehensive account of modern smooth ergodic theory, which provides a rigorous mathematical foundation for the phenomenon known as deterministic chaos -the appearance of 'chaotic' motions in pure deterministic dynamical systems.
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Ergodic properties of linear dynamical systems
TL;DR: The multiplicative ergodic theorem as mentioned in this paper states that for every invariant probability measure on a suitable base space, there is a measurable decomposition of the vector bundle over the base space into invariant measurable subbundles, and that every solution with initial conditions in any subbundle has strong Lyapunov exponents.
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Smoothness of spectral subbundles and reducibility of quasi-periodic linear differential systems
Russell Johnson,George R. Sell +1 more
TL;DR: In this paper, it was shown that the spectral subbundles are of class CN on the k-torus Tk under the full spectrum assumption and small divisors inequalities, and sufficient conditions in terms of smoothness were given in order that there is a coordinate system (z, ϑ) defined in the vicinity of Ω = H(φ), the hull of φ, so that the linearized system (1) can be represented in the form z′ = Dz and ϑ′ = ω, where D is a constant
References
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Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
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Lectures on Choquet's Theorem
TL;DR: The Krein-Milman theorem as an integral representation theorem has been applied to the metrizable case of the Choquet boundary as mentioned in this paper, and it has been used to define a new set of integral representation theorems for monotonic functions.
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Strict Ergodicity and Transformation of the Torus
TL;DR: In this paper, the authors consider the case that the transformation T of a compact Hausdorff space Q is strictly ergodic, i.e., it leaves invariant a unique probability measure on the borel field of the space.
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A Spectral Theory for Linear Differential Systems
Robert J. Sacker,George R. Sell +1 more
TL;DR: In this article, a spectral decomposition for a linear skew-product dynamical system is introduced and a perturbation theorem is proved that nearby systems have spectra which are close.