The geodesic flow on the unit cotangent bundle of the modular surface is intimately related to the continued fraction algorithm (see e.g. this article of 1,464 more words

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#### 246A, Notes 5: conformal mapping

In the previous set of notes we introduced the notion of a *complex diffeomorphism* between two open subsets of the complex plane (or more generally, two Riemann surfaces): an invertible holomorphic map whose inverse was also holomorphic. 13,364 more words

#### Math 246A, Notes 4: singularities of holomorphic functions

In the previous set of notes we saw that functions that were holomorphic on an open set enjoyed a large number of useful properties, particularly if the domain was simply connected. 11,838 more words