Stable and unstable manifolds of planar dynamical systems

- Definition of a phase portrait to a planar dynamical system and typical orbits.

- Definition of stable and unstable variets and description of their determination.

- Application of the Wazewski principle to a proof of the existence of a stable manifold.

- Examples of homoclinic and heteroclinic orbits.

- Determination of phase portraits to given planar dynamical systems.

- Creation of the phase portraits by a mathematical software.

Literature:

J.K.Hale, H. Kocak : Dynamics and Bifurcations, Springer, New York 1991.

L. Perko: Differential Equations and Dynamical Systems, Springer, New York 1993.

J.H. Hubbard, B.H. West: Differential Equations : A Dynamical Systems Approach, Springer, New York 1995.

J.Kalas, M. Ráb : Obyčejné diferenciální rovnice, MU Brno, 1995.

For students of the study course MAP