The Pesin identity shows that the Kolmogorov-Sinai entropy is equal to the sum of these in a dynamical system, while the Osedelec theorem gives them for an n-dimensional map. For Hamiltonian systems, they exist in additive invers pairs and one of these is always 0 for any system. They are never negative, which is why convergence of orbits is never observed in Hamiltonian systems, and a positive value for these values indicates that the system is not integrable. For ten points, what is this quantity, which describes the rate at which two initial
The Pesin identity shows that the Kolmogorov-Sinai entropy is equal to the sum of these in a dynamical system, while the Osedelec theorem gives them for an n-dimensional map. For Hamiltonian systems, they exist in additive invers pairs and one of these is always 0 for any system. They are never negative, which is why convergence of orbits is never observed in Hamiltonian systems, and a positive value for these values indicates that the system is not integrable. For ten points, what is this quantity, which describes the rate at which two initially-close trajectories diverge, a measure of chaos in a dynamical system?
The Pesin identity shows that the Kolmogorov-Sinai entropy is equal to the sum of these in a dynamical system, while the Osedelec theorem gives them for an n-dimensional map.
Lyapunov exponent