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]

Dendrite Julia set

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 $f(z) = z^2 + c$, then the Julia set of $f$ is a dendrite.^[3]

References

1. Whyburn, Gordon Thomas (1942), Analytic Topology, American Mathematical Society Colloquium Publications 28, New York: American Mathematical Society, p. 88, MR 0007095.
2. Carleson, Lennart; Gamelin, Theodore W. (1993), Complex Dynamics, Universitext 69, Springer, p. 94, ISBN 9780387979427.
3. Devaney, Robert L. (1989), An Introduction to Chaotic Dynamical Systems, Studies in Nonlinearity, Addison-Wesley Publishing Company, p. 294, MR 1046376.

See also

• 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