Dynamical systems and ergodic theory Basic notions Concept
Topological conjugacy
Summary
Two maps are topologically conjugate when a homeomorphism between their spaces turns one map into the other. Conjugate systems have the same dynamics up to a continuous change of coordinates: fixed points, periodic orbits, dense orbits and attractors correspond. Topological conjugacy is the basic notion of "same system" in topological dynamics, and many classification results, such as structural stability, are stated with it. If the homeomorphism is only required to be a continuous surjection, one gets the weaker notion of a semiconjugacy.
Where this leads
16 pages build on this one.
- Feigenbaum–Cvitanović functional equation
- External ray
- Poincaré classification of circle homeomorphisms
- Crisis
- Feigenbaum constants
- Intermittency
- Koenigs linearization theorem
- Bifurcation diagram
- Smale horseshoe
- Shilnikov theorem
- Denjoy theorem on rotation number
- Logistic map
- Bifurcation in a family of maps
- Jakobson's theorem
- Singer's theorem
- Böttcher's equation
Further reading
About this page
| Tag | HNXXAPQKG3 |
|---|---|
| URI | m2://HNXXAPQKG3 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 37C15, 37B02 |
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Used by
- Poincaré classification of circle homeomorphisms
- Koenigs linearization theorem
- Smale horseshoe
- Denjoy theorem on rotation number
- Logistic map
- Bifurcation in a family of maps
- Böttcher's equation