# 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

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