Lecturer(s)


MÁLEK Michal, doc. RNDr. Ph.D.

Course content

1. Elementary notions  orbit (full, forward, backward), fixed point, eventually fixed point, phase portrait, Brower fixed theorem, Sharkovskii ordering. 2. Hyperbolicity  critical point, hyperbolic point, attractive and repulsice point. 3. Quadratic system  logistic map, the tent map, rotations of the circle. 4. Symbolical dynamics  shift space and shift map. 5. Topological dynamics I.  minimal sets, limit sets, nonwandering sets, conjugacy. 6. Topological dynamics II.  transitivity, total transitivity, mixings, their relations and relations to the dense orbit. 7. Topological dynamics III.  recurrence and relations to ninimality. 8. Topological dynamics IV.  topological entropy.

Learning activities and teaching methods

unspecified

Recommended literature


H.Furstenberg. Recurrence in Ergodic Theory and Combinational Number Theory. Princeton University Press, Princeton, New Jersy, 1981.

J. Smítal. On functions and functional equations. Adam Hilger, Ltd., Bristol, 1988. ISBN 0852744188.

L. S. Block, W. A. Coppel. Dynamics in one dimension. Lecture Notes in Mathematics, 1513. SpringerVerlag, Berlin, 1992.

P. Walters. An introduction to ergodic theory. Graduate Texts in Mathematics, 79. SpringerVerlag, New YorkBerlin, 1982.

R. L. Devaney. An introduction to chaotic dynamical systems. Second edition, 1989.
