50 citations · 69 across the 10 of their papers we have counts for
12 papers
A remark on the phase transition for the geodesic flow of a rank one surface of nonpositive curvature
Keith Burns, Dong Chen
For any rank 1 nonpositively curved surface , it was proved by Burns-Climenhaga-Fisher-Thompson that for any , there exists a unique equilibrium state for , whe…
Phase transitions for the geodesic flow of a rank one surface with nonpositive curvature
Keith Burns, Jérôme Buzzi, Todd Fisher +1
We study the one parameter family of potential functions associated with the geometric potential for the geodesic flow of a compact rank 1 surface of nonpositive curva…
Unique equilibrium states for geodesic flows in nonpositive curvature
Keith Burns, Vaughn Climenhaga, Todd Fisher +1
We study geodesic flows over compact rank 1 manifolds and prove that sufficiently regular potential functions have unique equilibrium states if the singular set does not carry full…
Rates of mixing for the Weil-Petersson geodesic flow II: exponential mixing in exceptional moduli spaces
Keith Burns, Howard Masur, Carlos Matheus +1
We establish exponential mixing for the geodesic flow of an incomplete, negatively curved surface with cusp-like singularities of a prescribed order. A…
Average pace and horizontal chords
Keith Burns, Orit Davidovich, Diana Davis
We are motivated by a problem about running: If a race was completed in an average pace of P minutes per mile, is there necessarily some mile of the race that was run in exactly P…
Rates of mixing for the Weil-Petersson geodesic flow I: no rapid mixing in non-exceptional moduli spaces
Keith Burns, Howard Masur, Carlos Matheus +1
We show that the rate of mixing of the Weil-Petersson flow on non-exceptional (higher dimensional) moduli spaces of Riemann surfaces is at most polynomial.