Controlling chaos in higher dimensional maps with constant feedback: an analytical approach.
We introduce two methods to control chaos in higher-dimensional discrete maps with constant feedback. It is analytically shown for a general class of function vectors that chaotic attractors can be converted into fixed point attractors. Additionally, a method to choose an appropriate constant feedback is presented. The application of these methods does not require a priori knowledge of system equations, since time series information can be used. Desired periodic orbits can be accessed by varying the constant feedback. As an example, the methods are applied to the Hénon map.
Quantum Mechanics at Planck scale is considered as a deformation of the conventional Quantum Mechanics. Similar to the earlier works of the author, the main object of deformation is the density matrix. On this basis a notion of the entropy density is introduced that is a matrix value used for a detail study of the Information Problem at the Universe, and in particular, for the Information Paradox Problem.