Local Lyapunov Exponents

1. Front Matter

   Pages i-xvi

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2. Linear differential systems with parameter excitation

   Pages 9-51

3. Locality and time scales of the underlying non-degenerate stochastic system: Freidlin-Wentzell theory

   Pages 53-123

4. Exit probabilities for degenerate systems

   Pages 125-142

5. Local Lyapunov exponents

   Pages 143-229

6. Back Matter

   Pages 231-260

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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.

• degenerate diffusion
• exit probabilities
• metastability
• random perturbations of dynamical systems
• stochastic process
• sublimiting exponential growth rate
• ordinary differential equations

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)

• Allianz Lebensversicherungs - AG, Stuttgart, Germany

  Wolfgang Siegert

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