Dynamical systems and ergodic theory Basic notions Concept
Periodic point
Summary
A periodic point of a map is a point that comes back to itself after some positive number of steps. Its orbit is a finite cycle that repeats forever. Fixed points are the periodic points that return after one step. Periodic points are the simplest kind of long-time behaviour, and counting them says a lot about a system. For flows the analogue is a periodic orbit.
Where this leads
21 pages build on this one.
- Morse–Smale system
- Milnor–Thurston kneading theory
- Poincaré classification of circle homeomorphisms
- Spectral decomposition theorem
- Dynamical Mordell–Lang conjecture
- Artin–Mazur zeta function
- Period three implies chaos
- Closing lemma
- Siegel disc
- Arithmetic dynamics
- Classification of Fatou components
- Minimal period
- Smale's problems on dynamics
- Periodic solution of a difference equation
- Devaney chaos
- Axiom A
- Period-doubling bifurcation
- Jakobson's theorem
- Stability conjecture
- Singer's theorem
- Sharkovskii's theorem
Further reading
About this page
| Tag | T75CZ5H47N |
|---|---|
| URI | m2://T75CZ5H47N |
| Kind | concept |
| Writing | W0 stub |
| MSC | 37C25, 37B02, 37-01 |
| Same as |
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Used by
- Morse–Smale system
- Poincaré classification of circle homeomorphisms
- Dynamical Mordell–Lang conjecture
- Artin–Mazur zeta function
- Period three implies chaos
- Closing lemma
- Siegel disc
- Arithmetic dynamics
- Classification of Fatou components
- Minimal period
- Smale's problems on dynamics
- Periodic solution of a difference equation
- Devaney chaos
- Axiom A
- Period-doubling bifurcation
- Singer's theorem
- Sharkovskii's theorem