References
[1] A. Arroyo, F. Rodríguez Hertz, Homoclinic bifurcations and uniform hyperbolicity for three-dimensional flows, Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003) 805–841.
[2] Y. Assylbekov, N. Dairbekov, Hopf type rigidity for thermostats, Ergod. Th. \(\&\) Dynam. Sys 34 (2014) 1761–1769.
[3] Y. Benoist Convexes divisibles I, Algebraic groups and arithmetic, Tata Inst. Fund. Res., Mumbai, 2004, 339–374.
[4] Y. Benoist, D. Hulin, Cubic differentials and hyperbolic convex sets, J. of Differential Geom. 98 (2014) 1–19.
[5] J.-P. Benzécri, Sur les variétés localement affines et localement projectives, Bull. Soc. Math. France. 88 (1960), 229–332.
[6] A. Besse, Einstein manifolds, Classics in Mathematics, Springer Berlin, 1987.
[7] R. L. Bryant, Projectively flat Finsler \(2\)-spheres of constant curvature, Selecta Math. (N.S.) 3 (1997), 161–203.
[8] S. Choi and W.M. Goldman, Convex real projective structures on closed surfaces are closed, Proc. Amer. Math. Soc. 118 (1993) 657–661.
[9] N.S. Dairbekov, G.P. Paternain, Entropy production in Gaussian thermostats, Commun. Math. Phys. 269 (2007) 533–543.
[10] D. Dumas, M. Wolf, Polynomial cubic differentials and convex polygons in the projective plane, Geom. Funct. Anal. 25 (2015), 1734–1798.
[11] G. Gallavotti, New methods in nonequilibrium gases and fluids, Open Sys. Information Dynamics 6 (1999) 101–136.
[12] G. Gallavotti, D. Ruelle, SRB states and nonequilibrium statistical mechanics close to equilibrium, Commun. Math. Phys. 190 (1997) 279–281.
[13] É. Ghys, Flots d’Anosov sur les \(3\)-variétés fibrées en cercles, Ergodic Theory Dynam. Systems 4 (1984) 67–80.
[14] É. Ghys, Déformations de flots d’Anosov et de grupes fuchsiens, Ann. Inst. Fourier, 42 (1992) 209–247.
[15] É. Ghys, Rigidité différentiable des grupes fuchsiens, Publ. Math. IHES 78 (1993) 163–185.
[16] D. Gilbarg, N. S. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, Springer Berlin, 1998.
[17] W.M. Goldman. Convex real projective structures on compact surfaces, J. Differential Geom. 31 (1990) 791–845.
[18] N.J. Hitchin Lie groups and Teichmüller space, Topology 31 (1992) 449–473.
[19] N.J. Hitchin The self-duality equations on a Riemann surface, Proc. London Math. Soc. 55 (1987) 59–126.
[20] A. Katok, B. Hasselblatt, Introduction to the modern theory of dynamical systems, Encyclopedia of Mathematics and its Applications 54, Cambridge University Press, 1995.
[21] I. Kim, A. Papadopoulos, Convex real projective structures and Hilbert metrics, Handbook of Hilbert geometry, IRMA Lect. Math. Theor. Phys. 22, 2014, 307–338.
[22] D. Jane, G.P. Paternain, On the injectivity of the X-ray transform for Anosov thermostats, Discrete Contin. Dyn. Syst. 24 (2009) 471–487.
[23] S. Kobayashi, Differential geometry on complex vector bundles, Princeton University Press, 1987.
[24] F. Labourie, Anosov flows, surface groups and curves in projective space, Invent. Math. 165 (2006) 51–114.
[25] F. Labourie, Flat projective structures on surfaces and cubic holomorphic differentials, Pure Appl. Math. Q. 3 (2007) 1057–1099.
[26] F. Labourie, Cyclic surfaces and Hitchin components in rank 2, Ann. of Math. 185 (2017) 1–58.
[27] R. de la Llave, J.M. Marco, R. Moriyon, Canonical perturbation theory of Anosov systems and regularity for the Livsic cohomology equation, Ann. Math. 123 (1986) 537–611.
[28] J. Lewowicz, Lyapunov functions and topological stability, J. Diff. Equations 38 (1980) 192–209.
[29] J. C. Loftin, Affine spheres and convex \(\mathbb{RP}^n\)-manifolds, Amer. J. Math. 123 (2001) 255–274.
[30] T. Mettler, Extremal conformal structures on projective surfaces, arXiv:1510.01043
[31] T. Mettler, Minimal Lagrangian connections on compact surfaces, arXiv:1609.08033.
[32] T. Mettler, G.P. Paternain, Convex projective surfaces with compatible Weyl connection are hyperbolic, arXiv:1804.04616
[33] G.P. Paternain, Regularity of weak foliations for thermostats, Nonlinearity 20 (2007) 87–104.
[34] R. Potrie, A. Sambarino. Eigenvalues and entropy of a Hitchin representation, Invent. Math. 209 (2017) 885–925.
[35] D. Ruelle, Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics, J. Statist. Phys. 95 (1999) 393–468.
[36] V.A. Sharafutdinov, G. Uhlmann, On deformation boundary rigidity and spectral rigidity of Riemannian surfaces with no focal points, J. Diff. Geom. 56 (2000) 93–110.
[37] M.E. Taylor, Partial differential equations III. Nonlinear equations, 2nd Edition, Springer New York 2011.
[38] C. P. Wang, Some examples of complete hyperbolic affine \(2\)-spheres in \(\mathbb{R}^3\), Global differential geometry and global analysis, Lecture Notes in Math. 1481, Springer Berlin 1991, 271–280.
[39] A. Wienhard, An invitation to higher Teichmüller theory, arXiv:1803.06870
[40] M.P. Wojtkowski, Magnetic flows and Gaussian thermostats on manifolds of negative curvature, Fund. Math. 163 (2000) 177–191.
[41] M.P. Wojtkowski, W-flows on Weyl manifolds and Gaussian thermostats, J. Math. Pures Appl. 79 (2000) 953–974.
[42] M.P. Wojtkowski, Monotonicity, \({\mathcal J}\)-algebra of Potapov and Lyapunov exponents. Smooth ergodic theory and its applications (Seattle, WA, 1999), 499–521, Proc. Sympos. Pure Math. 69 Amer. Math. Soc., Providence, RI, 2001.