Dynamical Systems and Chaos
Explore iteration and flows; stability and bifurcations; chaos and long-term behavior. Concepts and connections are available independently of video coverage.
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Lyapunov exponents
Asymptotic growth rates quantify separation of nearby trajectories.
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Chaotic dynamics
Chaos combines forms of sensitive dependence and complex recurrence under specified definitions.
Equilibria and stability
Stability describes whether nearby trajectories remain close to or approach an equilibrium.
Ergodicity
In measure-preserving systems, ergodicity means invariant measurable sets have trivial measure.
Functions
A function assigns exactly one output to each input in its domain; its domain matters when comparing expressions.
Orbits
An orbit is the collection of states visited from a chosen initial state.
Knowledge connections
- Chaotic dynamics · Related · Map context
- Ergodicity · Related · Map context
- Equilibria and stability · Related · Map context
- Functions · Related · Map context
- Orbits · Prerequisite · Map context