Local Stable or Unstable Regions in 2-Dimensional Chaotic Forms: Examples and Simulations

We analyze 2-dimensional chaotic forms resulting from very simple systems based on two chaotic characteristics that is rotation and parallel movement or translation in geometric terms. Re ection is another alternative, along with rotation, for several interesting chaotic formations. Rotation and translation are very common types of movements in the world around us. Chaotic or non-chaotic forms arise from these two main generators. The rotation-translation chaotic case presented is based on the theory we analyzed in the book and in the paper†. An overview of the chaotic ows in rotation-translation is given. There is observed the presence of chaos when discrete rotation-translation equation forms are introduced. In such cases the continuous equations analogue of the discrete cases is useful. Characteristic cases and illustrations of chaotic attractors and forms are analyzed and simulated. The analysis of chaotic forms and attractors of the models presented is given along with an exploration of the characteristic or equilibrium points. Applications in the elds of astronomy-astrophysics (galaxies), chaotic advection (the sink problem) and Von Karman streets are presented.