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Establishing a new concept of local Lyapunov exponents the author brings together two separate theories, namely Lyapunov exponents and the theory of large deviations.
Specifically, a linear differential system is considered which is controlled by a stochastic process that during a suitable noise-intensity-dependent time is trapped near one of its so-called metastable states. The local Lyapunov exponent is then introduced as the exponential growth rate of the linear system on this time scale. Unlike classical Lyapunov exponents, which involve a limit as time increases to infinity in a fixed system, here the system itself changes as the noise intensity converges, too.
Specifically, a linear differential system is considered which is controlled by a stochastic process that during a suitable noise-intensity-dependent time is trapped near one of its so-called metastable states. The local Lyapunov exponent is then introduced as the exponential growth rate of the linear system on this time scale. Unlike classical Lyapunov exponents, which involve a limit as time increases to infinity in a fixed system, here the system itself changes as the noise intensity converges, too.
From the reviews:
"These lecture notes originate from the author's dissertation and provide a self-contained introduction to the notion of local Lyapunov exponents. ... provide a beautiful exposition to this partially subtle subject for readers acquainted with the theory of stochastic differential equations. ... Great qualities of this book are also the ample bibliography giving a representative state of the large literature in this field and the great amount of instructively worked out examples. ... The composition of the text is throughout clear, carefully thought through and harmonic." (Michael Högele, Zentralblatt MATH, Vol. 1178, 2010)
"These lecture notes originate from the author's dissertation and provide a self-contained introduction to the notion of local Lyapunov exponents. ... provide a beautiful exposition to this partially subtle subject for readers acquainted with the theory of stochastic differential equations. ... Great qualities of this book are also the ample bibliography giving a representative state of the large literature in this field and the great amount of instructively worked out examples. ... The composition of the text is throughout clear, carefully thought through and harmonic." (Michael Högele, Zentralblatt MATH, Vol. 1178, 2010)