# The differentiability of the hairs of ${\rm exp}(Z)$

@inproceedings{Silva1988TheDO, title={The differentiability of the hairs of \$\{\rm exp\}(Z)\$}, author={M. V. D. Silva}, year={1988} }

We prove that the hairs of the exponential-like maps f (z) = Aez are smooth curves. This answers affirmatively a question of Devaney and Krych. The proof is constructive in the sense that a dynamically defined CO' parametrization is presented. 0. Introduction. The study of the dynamical behaviour of the complex exponential map was begun by Fatou in 1926, following the work of Julia and Fatou himself concerning the dynamics of the rational maps on the sphere. Recently Devaney and Krych [DK] were… Expand

#### 13 Citations

Topological dynamics of exponential maps on their escaping sets

- Mathematics
- Ergodic Theory and Dynamical Systems
- 2006

On the differentiability of hairs for Zorich maps

- Mathematics
- Ergodic Theory and Dynamical Systems
- 2017

Parameter rays in the space of exponential maps

- Mathematics
- Ergodic Theory and Dynamical Systems
- 2009

#### References

SHOWING 1-5 OF 5 REFERENCES