Bounds on the number of non-simple closed geodesics on a surface

Abstract

We give bounds on the number of non-simple closed curves on a negatively curved surface, given upper bounds on both length and self-intersection number. In particular, it was previously known that the number of all closed curves of length at most $L$ grows exponentially in $L$. We get exponentially tighter bounds given weak conditions on self-intersection number.

References in corpus (1)

• Lower bound on the number of non-simple closed geodesics on surfaces

Cited by in corpus (4)

• Orbits of non-simple closed curves on a surface
• Counting Curves in Hyperbolic Surfaces
• Self intersections on a pair of pants
• Quantifying the sparseness of simple geodesics on hyperbolic surfaces