Integrability and Lyapunov Exponents
نویسنده
چکیده
A smooth distribution, invariant under a dynamical system, integrates to give an invariant foliation, unless certain resonance conditions are present.
منابع مشابه
On the Integrability of Intermediate
We study the integrability of intermediate distributions for Anosov diieomor-phisms and provide an example of C 1 ?Anosov diieomorphism on three dimensional torus whose intermediate stable foliation has leaves that admit only a nite number of derivatives. We also show that this phenomenon is quite abundant. In dimension four or higher this can happen even if the Lyapunov exponents at periodic o...
متن کاملOn the Integrability and Chaotic behaviour of an ecological model
A three species food chain model is studied analytically as well as numerically. Integrability of the model is studied using Painlevé analysis while chaotic behaviour is studied using numerical techniques, such as calculation of Lyapunov exponents, plotting the bifurcation diagram and phase plots. We correct and critically comment on the wrong results reported recently on this ecological model,...
متن کاملHölder Forms and Integrability of Invariant Distributions
Abstract. We prove an inequality for Hölder continuous differential forms on compact manifolds in which the integral of the form over the boundary of a sufficiently small, smoothly immersed disk is bounded by a certain multiplicative convex combination of the volume of the disk and the area of its boundary. This inequality has natural applications in dynamical systems, where Hölder forms are ub...
متن کاملSpurious 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...
متن کاملLyapunov 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 ....
متن کامل