Lectures on Lyapunov exponents

Lectures on Lyapunov Exponents and Smooth Ergodic Theory

1. Lyapunov Exponents for Differential Equations 2. Abstract Theory of Lyapunov Exponents 3. Regularity of Lyapunov Exponents Associated with Differential Equations 4. Lyapunov Stability Theory 5. The Oseledets Decomposition 6. Dynamical Systems with Nonzero Lyapunov Exponents. Multiplicative Ergodic Theorem 7. Nonuniform Hyperbolicity. Regular Sets 8. Examples of Nonuniformly Hyperbolic System...

Pisa Lectures on Lyapunov Exponents

Lyapunov Exponents and Strange Attractors in Discrete and Continuous Dynamical Systems

4 Lyapunov Exponents 5 4.1 Definition and basic properties . . . . 6 4.2 Constraints on the Lyapunov exponents 7 4.3 Calculating the largest Lyapunov exponent method 1 . . . . . . . . . . . 7 4.4 Calculating the largest Lyapunov exponent method 2 . . . . . . . . . . . 8 4.4.1 Maps . . . . . . . . . . . . . . 8 4.4.2 Continuous systems . . . . . . 8 4.5 Calculating the other Lyapunov exponents ....

Lyapunov Exponents of Systems Evolving on Quadratic Groups

In this paper we show some symmetry properties of Lyapunov exponents of a dynamical system when the linearized problem evolves on a quadratic group, X HX = H , with H orthogonal. It is well understood that in this case the exponents are symmetric with respect to the origin. Here, we give lower bounds on the number of Lyapunov exponents which are 0, and show that some Lyapunov exponents may have...

Spurious Lyapunov Exponents Computed Using the Eckmann - Ruelle Procedure

Lyapunov exponents, important invariants of a complicated dynamical process, can be difficult to determine from experimental data. In particular, when using embedding theory to build chaotic attractors in a reconstruction space, extra “spurious” Lyapunov exponents can arise that are not Lyapunov exponents of the original system. By studying the local linearization matrices that are key to a pop...