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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Ergodicity
In measure-preserving systems, ergodicity means invariant measurable sets have trivial measure.
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Attractors
An attractor is an invariant set approached by a specified collection of trajectories.
Lyapunov exponents
Asymptotic growth rates quantify separation of nearby trajectories.
Bifurcations
Changing a parameter can qualitatively change equilibria or periodic behavior.
Chaotic dynamics
Chaos combines forms of sensitive dependence and complex recurrence under specified definitions.
Continuous flows
An autonomous differential equation generates time-indexed state transformations where solutions exist uniquely.
Knowledge connections
- Attractors · Related · Map context
- Lyapunov exponents · Related · Map context