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Dynamical Systems

Dynamical SystemsDynamical systems is the study of processes that evolve over time. It is assumed that this evolution is deterministic, meaning that if the current state of the process is specified, then all future states of the process are determined.

A dynamical system involves a state space and a rule, the generator of the system, that expresses how a choice of a current state determines all future states the collection of which is called orbit. Questions that are typically addressed are:

  1. Sensitivity to initial conditions: How does an orbit of a dynamical system change if the initial point is changed slightly?
  2. How do the collection of orbits of the dynamical system change if the generator is changed slightly?

In dealing with such questions, we often look for answers in terms of special properties of orbits, such as periodicity and recurrence. The questions that are addressed are qualitative, often dealing with the long-term behavior of “most” orbits, as opposed to trying to obtain exact formulas for one orbit.



Michael Hurley