Tutorial: Some examples of chaotic systems скачать в хорошем качестве

Tutorial: Some examples of chaotic systems

In this lecture, we will see a definition of chaotic dynamics, and several examples of systems which can be proven to be chaotic according to this definition. The last example, Smale's horseshoe maps, is useful in the study of more realistic systems, and we give two examples of that as well. Intro: 0:00 What is a chaotic system? 0:28 Example 1 - The dyadic transformation: 5:42 Example 2 - The tent map: 28:32 Example 3 - The logistic map: 34:03 Example 4 - The tent map with slope 3: 39:31 Example 5 - Arnold's cat map: 49:38 Example 6 - Smale's horseshoe map: 56:02 Homoclinic intersections: 1:04:38 Silnikov's mechanism: 1:09:21 Related lecture notes (in particular chapter 4): https://arxiv.org/abs/math.HO/0111177 Dispersive billiards:    • Sinai and similar dispersing billiards   Stadium billiard:    • Billiards in a stadium   Stability of periodic orbits:    • Tutorial: Stability of periodic orbits - a...   #chaos #fractal #CantorSet #horseshoe_map