3. Specific Examples

Problem 3.1.
[Keith Burns] Let $\varphi_1,\varphi_2 : X \to \R$ be two potentials. What interesting analysis can be said about the 2parameter family of equilibrium states $\mu_{q_1\varphi_1 + q_2\varphi_2}$? Can we find useful applications for these results? 
Problem 3.2.
[Todd Fisher] Generalize the results of Bufetov and Gurevich in [MR2857792] to the space of quadratic differentials. 
Problem 3.3.
[Todd Fisher and Keith Burns] What can be said about interesting phase transitions for potentials $\{q\varphi\}_{q\in\R}$? In particular, let $M$ be a compact surface of nonpositive curvature, and $\varphi$ be the geometric potential, so that $q = 1$ is a phase transition. 
Problem 3.4.
[Yuri Lima] Consider a dynamical billiard without cusps. Do (nonperiodic) invariant probability measures for the billiard map satisfy the integrability condition for Oseledetâ€™s theorem? 
Problem 3.5.
[Vaughn Climenhaga] Are there examples of nonuniformly hyperbolic magnetic flows for which we can apply the tools of thermodynamical formalism? 
Problem 3.6.
[Kurt Vinhage] Study the measure of maximal entropy for the HandelThurston Anosov flow. Does it coincide with Lebesgue measure? If not, what is its dimension? 
Problem 3.7.
[Jermoe Buzzi] Can one identify a geometric example of a system for which the set of phase transitions has positive Lebesgue measure?
Cite this as: AimPL: Equilibrium states for dynamical systems arising from geometry, available at http://aimpl.org/equibdynsysgeom.