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The study of the behavior of dynamical systems where the phase space is a topological space, focusing on the properties that are invariant under homeomorphisms.

A system in which a function describes the time dependence of a point in a geometrical space.

A continuous function between topological spaces that has a continuous inverse function, preserving topological properties.

The set of all points that can be reached by iterating a function from one particular point in the space.

A set towards which a dynamical system evolves over time, typically where the system is stable.

A point in the phase space of a dynamical system where the system can remain indefinitely without changing state.

An orbit that repeats itself after some period, indicating that the system returns to its original state.

A qualitative change in the behavior of a dynamical system as a parameter is varied, resulting in the sudden appearance or disappearance of one or more solutions.

Behavior exhibited by deterministic systems that are highly sensitive to initial conditions, making long-term prediction impossible.