A Caltech Library Service

Modular curves, C^* algebras, and chaotic cosmology

Marcolli, Matilde (2003) Modular curves, C^* algebras, and chaotic cosmology. . (Submitted)

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


We make some brief remarks on the relation of the mixmaster universe model of chaotic cosmology to the geometry of modular curves and to noncommutative geometry. We show that the full dynamics of the mixmaster universe is equivalent to the geodesic flow on the modular curve X_(Γ0(2)). We then consider a special class of solutions, with bounded number of cycles in each Kasner era, and describe their dynamical properties (invariant density, Lyapunov exponent, topological pressure). We relate these properties to the noncommutative geometry of a moduli space of such solutions, which is given by a Cuntz–Krieger C^∗-algebra.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Additional Information:(Submitted on 11 Dec 2003)
Record Number:CaltechAUTHORS:20170713-082602443
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79062
Deposited By: Ruth Sustaita
Deposited On:13 Jul 2017 16:28
Last Modified:01 Jun 2023 23:58

Repository Staff Only: item control page