Dendrite (mathematics)
In mathematics, a dendrite is a certain type of topological space that may be characterized either as a locally connected dendroid or equivalently as a locally connected continuum that contains no simple closed curves.^{[1]}
Importance
Dendrites may be used to model certain types of Julia set.^{[2]} For example, if 0 is pre-periodic, but not periodic, under the function , then the Julia set of is a dendrite.^{[3]}
References
- ^ Whyburn, Gordon Thomas (1942), Analytic Topology, American Mathematical Society Colloquium Publications, 28, New York: American Mathematical Society, p. 88, MR 0007095.
- ^ Carleson, Lennart; Gamelin, Theodore W. (1993), Complex Dynamics, Universitext, 69, Springer, p. 94, ISBN 9780387979427.
- ^ Devaney, Robert L. (1989), An Introduction to Chaotic Dynamical Systems, Studies in Nonlinearity, Addison-Wesley Publishing Company, p. 294, MR 1046376.
See also
Wikimedia Commons has media related to Dendrite Julia sets. |
- Misiurewicz point
- Real tree, a related concept defined using metric spaces instead of topological spaces
- Dendroid (topology) and unicoherent space, two more general types of tree-like topological space
This topology-related article is a stub. You can help Wikipedia by expanding it. |
This page is based on the copyrighted Wikipedia article "Dendrite (mathematics)"; it is used under the Creative Commons
Attribution-ShareAlike 3.0 Unported License (CC-BY-SA). You may
redistribute it, verbatim or modified, providing that you comply with
the terms of the CC-BY-SA