# Dimension

## Two lectures. Dimensional analysis or paradise in physics

In the two lectures read at school for senior pupils «Nonlinear days in Saratov for youth» the basic definitions of the theory of dimension and similarity are stated, and also some special ways for concrete problems decision, in particular, use Pi-theorem and additions of Huntley are presented. The solutions of problems from different areas of physics are shown.

## Entropy and forecasting of time series in the theory of dynamical systems

A contemporary consideration of such concepts as dimension and entropy of dynamical systems is given. Description of these characteristics includes into the analysis the other notions and properties related to complicated behavior of nonlinear systems as embedding dimension, prediction horizon etc., which are used in the paper. A question concerning the application of these ideas to real observables of the economical origin, i.e. market prices of the companies Schlumberger, Deutsche Bank, Honda, Toyota, Starbucks, BP is studied.