Local Lyapunov exponents : sublimiting growth rates of linear random differential equations

• Main Author: Siegert, Wolfgang.
• Format: Book
• Published: Springer 2017
• Subjects: Mathematics and Statistics ; Lyapunov exponents ; Differential equations.; 515.35
• Online Access: http://repository.vnu.edu.vn/handle/VNU_123/31961
• Institution: Vietnam National University, Hanoi

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.