منابع مشابه
Evans function and Fredholm determinants
We explore the relationship between the Evans function, transmission coefficient and Fredholm determinant for systems of first-order linear differential operators on the real line. The applications we have in mind include linear stability problems associated with travelling wave solutions to nonlinear partial differential equations, for example reaction-diffusion or solitary wave equations. The...
متن کاملEvans Functions, Jost Functions, and Fredholm Determinants
The principal results of this paper consist of an intrinsic definition of the Evans function in terms of newly introduced generalized matrix-valued Jost solutions for general first-order matrix-valued differential equations on the real line, and a proof of the fact that the Evans function, a finite-dimensional determinant by construction, coincides with a modified Fredholm determinant associate...
متن کامل2-modified characteristic Fredholm determinants, Hill’s method, and the periodic Evans function of Gardner
Using the relation established by Johnson–Zumbrun between Hill’s method of aproximating spectra of periodic-coefficient ordinary differential operators and a generalized periodic Evans function given by the 2-modified characteristic Fredholm determinant of an associated Birman–Schwinger system, together with a Volterra integral computation introduced by Gesztesy–Makarov, we give an explicit con...
متن کاملDerivatives of the Evans function and (modified) Fredholm determinants for first order systems
The Evans function is a Wronskian type determinant used to detect point spectrum of differential operators obtained by linearizing PDEs about special solutions such as traveling waves, etc. This work is a sequel to the paper “Derivatives of (modified) Fredholm determinants and stability of standing and traveling waves”, published by F. Gesztesy, K. Zumbrun and the second author in J. Math. Pure...
متن کاملIntermittency and Regularized Fredholm Determinants
We consider real-analytic maps of the interval I = [0, 1] which are expanding everywhere except for a neutral fixed point at 0. We show that on a certain function space the spectrum of the associated Perron-Frobenius operator M has a decomposition sp(M) = σc ∪ σp where σc = [0, 1] is the continuous spectrum of M and σp is the pure point spectrum with no points of accumulation outside 0 and 1. W...
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ژورنال
عنوان ژورنال: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
سال: 2015
ISSN: 1364-5021,1471-2946
DOI: 10.1098/rspa.2014.0597