M. Pettini, Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics, IAM Series n, 2007.
DOI : 10.1007/978-0-387-49957-4

URL : http://arxiv.org/pdf/0711.1484v2.pdf

M. Cerruti-sola, G. Ciraolo, R. Franzosi, and M. Pettini, Riemannian geometry of Hamiltonian chaos: Hints for a general theory, Physical Review E, vol.30, issue.4, p.46205, 2008.
DOI : 10.1103/PhysRevE.68.036120

L. Caiani, L. Casetti, C. Clementi, G. Pettini, M. Pettini et al., Geometry of dynamics and phase transitions in classical lattice ? 4 theories, Phys.Rev, vol.57, p.3886, 1998.

L. Casetti, M. Pettini, and E. G. Cohen, Geometric approach to Hamiltonian dynamics and statistical mechanics, Physics Reports, vol.337, issue.3, p.237, 2000.
DOI : 10.1016/S0370-1573(00)00069-7

URL : http://arxiv.org/pdf/cond-mat/9912092

R. Franzosi and M. Pettini, Theorem on the Origin of Phase Transitions, Physical Review Letters, vol.267, issue.6, p.60601, 2004.
DOI : 10.1038/31146

R. Franzosi, L. Spinelli, and M. Pettini, Topology and phase transitions I. Preliminary results, Nuclear Physics B, vol.782, issue.3, p.189, 2007.
DOI : 10.1016/j.nuclphysb.2007.04.025

URL : https://hal.archives-ouvertes.fr/hal-00145212

R. Franzosi and M. Pettini, Topology and phase transitions II. Theorem on a necessary relation, Nuclear Physics B, vol.782, issue.3, p.219, 2007.
DOI : 10.1016/j.nuclphysb.2007.04.035

R. Franzosi and R. Franzosi, Microcanonical entropy and dynamical measure of temperature for systems with two first integrals Geometric microcanonical thermodynamics for systems with first integrals, J. Stat. Phys. Phys. Rev. E85, vol.143, issue.824, p.50101, 2011.

G. Carlsson, J. Gorham, M. Kahle, and J. Mason, Computational topology for configuration spaces of hard disks, Physical Review E, vol.6, issue.1, p.11303, 2012.
DOI : 10.1007/s00222-010-0303-6

Y. Baryshnikov, P. Bubenik, and M. Kahle, Min-Type Morse Theory for Configuration Spaces of Hard Spheres, International Mathematics Research Notices, vol.70, issue.1, 2013.
DOI : 10.1103/PhysRevE.70.016113

D. C. Brody, D. W. Hook, and L. P. Hughston, Quantum phase transitions without thermodynamic limits, Proc. Roy. Soc. A (London), p.2021, 2007.
DOI : 10.1098/rspa.2007.1865

URL : http://rspa.royalsocietypublishing.org/content/royprsa/463/2084/2021.full.pdf

P. Buonsante, R. Franzosi, and A. Smerzi, Phase transitions at high energy vindicate negative microcanonical temperature, Physical Review E, vol.95, issue.5
DOI : 10.1103/PhysRevE.85.050101

URL : http://arxiv.org/pdf/1506.01933

G. E. Volovik, Quantum phase transitions from topology in momentum space, in Quantum analogues : from phase transitions to black holes and cosmology, pp.31-73, 2007.

L. Angelani, R. Di-leonardo, G. Parisi, and G. Ruocco, Topological Description of the Aging Dynamics in Simple Glasses, Physical Review Letters, vol.55, issue.5, p.55502, 2001.
DOI : 10.1103/PhysRevE.55.3705

P. G. Debenedetti and F. H. Stillinger, Supercooled liquids and the glass transition, Nature, vol.102, issue.6825, p.259, 2001.
DOI : 10.1021/jp973144h

S. Risau-gusman, A. C. Ribeiro-teixeira, D. A. Stariolo, and T. , Topology, Phase Transitions, and the Spherical Model, phase transitions, and the spherical model, p.145702, 2005.
DOI : 10.1103/PhysRevE.70.036125

URL : http://arxiv.org/pdf/cond-mat/0508419

D. A. Garanin, R. Schilling, and A. Scala, Saddle index properties, singular topology, and its relation to thermodynamic singularities for a ? 4 mean-field model, Phys. Rev, vol.70, p.36125, 2004.

F. A. Santos, L. C. Da-silva, and M. D. , Topological approach to microcanonical thermodynamics and phase transition of interacting classical spins, Journal of Statistical Mechanics: Theory and Experiment, vol.2017, issue.1, p.13202, 2017.
DOI : 10.1088/1742-5468/2017/1/013202

P. Grinza and A. Mossa, Topological Origin of the Phase Transition in a Model of DNA Denaturation, Physical Review Letters, vol.11, issue.15, p.158102, 2004.
DOI : 10.1209/epl/i2003-00439-9

O. M. Becker and M. Karplus, The topology of multidimensional potential energy surfaces: Theory and application to peptide structure and kinetics, The Journal of Chemical Physics, vol.27, issue.4, p.1495, 1997.
DOI : 10.1002/(SICI)1097-0134(199702)27:2<213::AID-PROT8>3.0.CO;2-G

M. Bachmann, Thermodynamics and Statistical Mechanics of Macromolecular Systems, 2014.
DOI : 10.1017/CBO9781139028516

G. Carlsson and A. Zomorodian, Persistent homology -a survey, Discrete Comput, Geom. Carlsson, Topology and data, Bull. Am. Math. Soc, vol.33, issue.2, p.255, 2005.

I. Donato, M. Gori, M. Pettini, G. Petri, S. De-nigris et al., Vaccarino Persistent Homology analysis of Phase Transitions, Phys. Rev, vol.93, p.52138, 2016.

M. Kastner and D. Mehta, Phase Transitions Detached from Stationary Points of the Energy Landscape, Physical Review Letters, vol.107, issue.16, p.160602, 2011.
DOI : 10.1103/PhysRevE.84.025702

D. Ruelle, Thermodynamic Formalism, Encyclopaedia of Mathematics and Its Applications, 1978.

C. Sormani and H. Riemannian-manifolds-converge, Metric and Differential Geometry, Progress in Mathematics Birkhäuser, vol.297, 2012.

L. Caiani, L. Casetti, and M. Pettini, Hamiltonian dynamics of the two-dimensional lattice model, Journal of Physics A: Mathematical and General, vol.31, issue.15, p.3357, 1998.
DOI : 10.1088/0305-4470/31/15/004

L. Casetti, Efficient symplectic algorithms for numerical simulations of Hamiltonian flows, Physica Scripta, vol.51, issue.1, p.29, 1995.
DOI : 10.1088/0031-8949/51/1/005

M. Kac, On the notion of recurrence in discrete stochastic processes, Bulletin of the American Mathematical Society, vol.53, issue.10, pp.1002-1010, 1947.
DOI : 10.1090/S0002-9904-1947-08927-8

P. Varandas, A version of Kac???s lemma on first return times for suspension flows, Stochastics and Dynamics, vol.128, issue.02, p.1660002, 2016.
DOI : 10.1142/S0129055X09003785

J. K. Moser, Lectures on Hamiltonian systems, Mem. Am. Math. Soc, vol.81, pp.1-60, 1968.

G. Benettin and A. Giorgilli, On the Hamiltonian interpolation of near-to-the identity symplectic mappings with application to symplectic integration algorithms, Journal of Statistical Physics, vol.73, issue.5-6, pp.1117-1143, 1994.
DOI : 10.1007/BF02188219

M. Ledoux, The Concentration of Measure Phenomenon, Mathematical Surveys and Monographs, vol.89, 2001.
DOI : 10.1090/surv/089

M. Gromov, Isoperimetric inequalities in Riemannian manifolds, Appendix I to V. D. Milman and G. Schechtman, Asymptotic Theory of Finite Dimensional Normed Spaces, Lecture Notes Math, vol.1200, 1986.

V. Bayle, Propriétés de concavité du profil isopérimétrique et applications, Diss. Universit? Joseph-Fourier-Grenoble I, 2003.

F. Morgan, Manifolds with density, Notices of the AMS, pp.853-858, 2005.

J. A. Thorpe, Elementary Topics in Differential Geometry, p.55, 1979.
DOI : 10.1007/978-1-4612-6153-7

M. Rasetti, Topological Concepts in Phase Transition Theory, in Differential Geometric Methods in Mathematical Physics, 1979.

M. Rasetti, Structural Stability in Statistical Mechanics, Structural Stability in Physics, p.159, 1979.
DOI : 10.1007/978-3-642-67363-4_16