One of the major achievements of the 20th century science was understanding that purely deterministic systems may behave similarly to purely random (stochastic) systems. This area was loosely called a chaos theory.

Because, starting from the very beginning, the statements of this theory contradicted uniformly accepted in scientific (even physics) community ideology and intuition, convincing results must be rigorously proved.

Essentially these results deal with introducing new classes of dynamical (deterministic) systems with more and more “surprising” behavior. I will describe major ideas and results in the area including some latest (once again, “surprising”) results.

The exposition will be visual and elementary with very few formulas used. Math and physics students are welcomed.