Loading Web-Font TeX/Math/Italic
| Register
\newcommand{\Cat}{{\rm Cat}} \newcommand{\A}{\mathcal A} \newcommand{\freestar}{ \framebox[7pt]{$\star$} }

3. Specific Examples


    1. Add remark

      Problem 3.1.

      [Keith Burns] Let \varphi_1,\varphi_2 : X \to \R be two potentials. What interesting analysis can be said about the 2-parameter family of equilibrium states \mu_{q_1\varphi_1 + q_2\varphi_2}? Can we find useful applications for these results?


        • Add remark

          Problem 3.2.

          [Todd Fisher] Generalize the results of Bufetov and Gurevich in [MR2857792] to the space of quadratic differentials.


            • Add remark

              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.


                • Add remark

                  Problem 3.4.

                  [Yuri Lima] Consider a dynamical billiard without cusps. Do (non-periodic) invariant probability measures for the billiard map satisfy the integrability condition for Oseledet’s theorem?


                    • Add remark

                      Problem 3.5.

                      [Vaughn Climenhaga] Are there examples of non-uniformly hyperbolic magnetic flows for which we can apply the tools of thermodynamical formalism?


                        • Add remark

                          Problem 3.6.

                          [Kurt Vinhage] Study the measure of maximal entropy for the Handel-Thurston Anosov flow. Does it coincide with Lebesgue measure? If not, what is its dimension?


                            • Add remark

                              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.