References

[1] A. Arroyo, F. Rodriguez Hertz, Homoclinic bifurcations and uniform hyperbolicity for three-dimensional flows, Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003), 805–841. MR zbM

[2] M. Asaoka, Regular projectively Anosov flows on three-dimensional manifolds, Ann. Inst. Fourier (Grenoble) 60 (2010), 1649–1684. MR zbM

[3] Y. Benoist, Convexes divisibles. I, in Algebraic groups and arithmetic, Tata Inst. Fund. Res., Mumbai, 2004, pp. 339–374. MR zbM

[4] J. Bochi, N. Gourmelon, Some characterizations of domination, Math. Z. 263 (2009), 221–231. MR zbM

[5] J. Bochi, R. Potrie, A. Sambarino, Anosov representations and dominated splittings, J. Eur. Math. Soc. (JEMS) 21 (2019), 3343–3414. MR zbM

[6] C. Bonatti, L. J. Dı́az, M. Viana, Dynamics beyond uniform hyperbolicity, Encyclopaedia of Mathematical Sciences 102, Springer-Verlag, Berlin, 2005, A global geometric and probabilistic perspective, Mathematical Physics, III. MR zbM

[7] S. B. Bradlow, Vortices in holomorphic line bundles over closed Kähler manifolds, Comm. Math. Phys. 135 (1990), 1–17. MR zbM

[8] R. L. Bryant, Projectively flat Finsler \(2\)-spheres of constant curvature, Selecta Math. (N.S.) 3 (1997), 161–203. MR zbM

[9] K. Cieliebak, A. R. Gaio, I. Mundet i Riera, D. A. Salamon, The symplectic vortex equations and invariants of Hamiltonian group actions, J. Symplectic Geom. 1 (2002), 543–645. MR zbM

[10] S. Crovisier, R. Potrie, Introduction to partially hyperbolic dynamics, in School on Dynamical Systems, International Centre for Theoretical Physics, Trieste, 2015.

[11] M. Dunajski, Abelian vortices from sinh-Gordon and Tzitzeica equations, Phys. Lett. B 710 (2012), 236–239. MR

[12] Y. M. Eliashberg, W. P. Thurston, Confoliations, University Lecture Series 13, American Mathematical Society, Providence, RI, 1998. MR zbM

[13] G. Gallavotti, New methods in nonequilibrium gases and fluids, Open Syst. Inf. Dyn. 6 (1999), 101–136. MR zbM

[14] G. Gallavotti, D. Ruelle, SRB states and nonequilibrium statistical mechanics close to equilibrium, Comm. Math. Phys. 190 (1997), 279–285. MR zbM

[15] H. Geiges, J. Gonzalo Pérez, Generalised spin structures on 2-dimensional orbifolds, Osaka J. Math. 49 (2012), 449–470. MR zbM

[16] E. Ghys, Flots d’Anosov sur les \(3\)-variétés fibrées en cercles, Ergodic Theory Dynam. Systems 4 (1984), 67–80. MR zbM

[17] N. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3) 55 (1987), 59–126. MR zbM

[18] E. Hopf, Closed surfaces without conjugate points, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 47–51. MR zbM

[19] A. Jaffe, C. Taubes, Vortices and monopoles, Progress in Physics 2, Birkhäuser, Boston, Mass., 1980, Structure of static gauge theories. MR zbM

[20] I. Kim, A. Papadopoulos, Convex real projective structures and Hilbert metrics, in Handbook of Hilbert geometry, IRMA Lect. Math. Theor. Phys. 22, Eur. Math. Soc., Zürich, 2014, pp. 307–338. MR

[21] F. Labourie, Anosov flows, surface groups and curves in projective space, Invent. Math. 165 (2006), 51–114. MR zbM

[22] F. Labourie, Flat projective structures on surfaces and cubic holomorphic differentials, Pure Appl. Math. Q. 3 (2007), 1057–1099. MR zbM

[23] J. C. Loftin, Affine spheres and convex \(\mathbb{RP}^n\)-manifolds, Amer. J. Math. 123 (2001), 255–274. MR zbM

[24] T. Mettler, Minimal Lagrangian connections on compact surfaces, Adv. Math. 354 (2019), Article ID 106747, 36 pp. MR zbM

[25] T. Mettler, G. P. Paternain, Holomorphic differentials, thermostats and Anosov flows, Math. Ann. 373 (2019), 553–580. MR zbM

[26] T. Mettler, G. P. Paternain, Convex projective surfaces with compatible Weyl connection are hyperbolic, Anal. PDE 13 (2020), 1073–1097. MR zbM

[27] Y. Mitsumatsu, Anosov flows and non-Stein symplectic manifolds, Ann. Inst. Fourier (Grenoble) 45 (1995), 1407–1421. MR zbM

[28] M. Noguchi, Yang-Mills-Higgs theory on a compact Riemann surface, J. Math. Phys. 28 (1987), 2343–2346. MR zbM

[29] D. Ruelle, Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics, J. Statist. Phys. 95 (1999), 393–468. MR zbM

[30] M. Sambarino, A (short) survey on dominated splittings, in Mathematical Congress of the Americas, Contemp. Math. 656, Amer. Math. Soc., Providence, RI, 2016, pp. 149–183. MR zbM

[31] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817. MR zbM

[32] M. E. Taylor, Partial differential equations III. Nonlinear equations, second ed., Applied Mathematical Sciences 117, Springer, New York, 2011. MR zbM

[33] M. P. Wojtkowski, Magnetic flows and Gaussian thermostats on manifolds of negative curvature, Fund. Math. 163 (2000), 177–191. MR zbM

[34] M. P. Wojtkowski, \(W\)-flows on Weyl manifolds and Gaussian thermostats, J. Math. Pures Appl. (9) 79 (2000), 953–974. MR zbM

[35] M. P. Wojtkowski, Monotonicity, \(\mathcal{J}\)-algebra of Potapov and Lyapunov exponents, in Smooth ergodic theory and its applications (Seattle, WA, 1999), Proc. Sympos. Pure Math. 69, Amer. Math. Soc., Providence, RI, 2001, pp. 499–521. MR zbM