## Involve: A Journal of Mathematics

• Involve
• Volume 10, Number 1 (2017), 151-164.

### Loewner deformations driven by the Weierstrass function

#### Abstract

The Loewner differential equation provides a way of encoding growing families of sets into continuous real-valued functions. Most famously, Schramm–Loewner evolution (SLE) consists of the growing random families of sets that are encoded via the Loewner equation by a multiple of Brownian motion. The purpose of this paper is to study the families of sets encoded by a multiple of the Weierstrass function, which is a deterministic analog of Brownian motion. We prove that there is a phase transition in this setting, just as there is in the SLE setting.

#### Article information

Source
Involve, Volume 10, Number 1 (2017), 151-164.

Dates
Accepted: 13 December 2015
First available in Project Euclid: 22 November 2017

https://projecteuclid.org/euclid.involve/1511371088

Digital Object Identifier
doi:10.2140/involve.2017.10.151

Mathematical Reviews number (MathSciNet)
MR3561735

Zentralblatt MATH identifier
1357.30004

Subjects
Primary: 30C35: General theory of conformal mappings

#### Citation

Lind, Joan; Robins, Jessica. Loewner deformations driven by the Weierstrass function. Involve 10 (2017), no. 1, 151--164. doi:10.2140/involve.2017.10.151. https://projecteuclid.org/euclid.involve/1511371088

#### References

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