G. Allaire, Analyse numérique et optimisation, 2005.

R. Aurich and F. Steiner, Periodic-orbit sum rules for the Hadamard-Gutzwiller model, Physica D: Nonlinear Phenomena, vol.39, issue.2-3, pp.169-193, 1989.
DOI : 10.1016/0167-2789(89)90003-1

R. Aurich and F. Steiner, Statistical properties of highly excited quantum eigenstates of a strongly chaotic system, Physica D: Nonlinear Phenomena, vol.64, issue.1-3, pp.185-214, 1993.
DOI : 10.1016/0167-2789(93)90255-Y

N. L. Balazs and A. Voros, Chaos on the pseudosphere, Physics Reports, vol.143, issue.3, pp.109-240, 1986.
DOI : 10.1016/0370-1573(86)90159-6

P. C. Bressloff, N. W. Bressloff, and J. D. Cowan, Dynamical Mechanism for Sharp Orientation Tuning in an Integrate-and-Fire Model of a Cortical Hypercolumn, Neural Computation, vol.16, issue.11, pp.2473-2511, 2000.
DOI : 10.1007/BF00288786

P. C. Bressloff, J. D. Cowan, M. Golubitsky, P. J. Thomas, and M. C. Wiener, Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex, Philosophical Transactions of the Royal Society B: Biological Sciences, vol.356, issue.1407, pp.306299-330, 1407.
DOI : 10.1098/rstb.2000.0769

P. C. Bressloff, J. D. Cowan, M. Golubitsky, P. J. Thomas, and M. C. Wiener, What Geometric Visual Hallucinations Tell Us about the Visual Cortex, Neural Computation, vol.222, issue.8, pp.473-491, 2002.
DOI : 10.1007/BF00288786

S. A. Broughton, Classifying finite group actions on surfaces of low genus, Journal of Pure and Applied Algebra, vol.69, issue.3, pp.233-270, 1991.
DOI : 10.1016/0022-4049(91)90021-S

S. A. Broughton, R. M. Dirks, M. T. Sloughter, and C. R. Vinroot, Triangular surface tiling groups for low genus, 2001.

P. Buser, Geometry and spectra of compact Riemann surfaces, 1992.
DOI : 10.1007/978-0-8176-4992-0

P. Chossat and O. Faugeras, Hyperbolic Planforms in Relation to Visual Edges and Textures Perception, PLoS Computational Biology, vol.33, issue.12, p.1000625, 2009.
DOI : 10.1371/journal.pcbi.1000625.s006
URL : https://hal.archives-ouvertes.fr/hal-00807344

P. Chossat and R. Lauterbach, Methods in Equivariant Bifurcations and Dynamical Systems, 2000.
DOI : 10.1142/4062

P. G. Ciarlet and J. L. Lions, Handbook of Numerical Analysis. Volume II. Finite Element Methods (part1), 1991.

N. J. Cornish and D. Spergel, On the eigenmodes of compact hyperbolic 3-manifolds, 1999.

N. J. Cornish and N. Turok, Ringing the eigenmodes from compact manifolds, Classical and Quantum Gravity, vol.15, issue.9, 1998.
DOI : 10.1088/0264-9381/15/9/016
URL : http://arxiv.org/abs/gr-qc/9802066

P. Dayan and L. F. Abbott, Theoretical Neuroscience : Computational and Mathematical Modeling of Neural Systems, 2001.

B. Dionne and M. Golubitsky, Planforms in two and three dimensions, ZAMP Zeitschrift f???r angewandte Mathematik und Physik, vol.1, issue.No. 4, pp.36-62, 1992.
DOI : 10.1007/BF00944740

B. Ermentrout, Neural networks as spatio-temporal pattern-forming systems, Reports on Progress in Physics, vol.61, issue.4, pp.353-430, 1998.
DOI : 10.1088/0034-4885/61/4/002
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.16.6053

A. Fässler and E. L. Stiefel, Group theoretical methods and their applications, 1992.

M. Golubitsky, I. Stewart, and D. G. Schaeffer, Singularities and Groups in Bifurcation Theory, 1988.

D. Gorenstein, Finite groups, 1980.

D. Hansel and H. Sompolinsky, Modeling feature selectivity in local cortical circuits. Methods of neuronal modeling, pp.499-567, 1997.

S. Helgason, Groups and geometric analysis, volume 83 of Mathematical Surveys and Monographs, 2000.

R. B. Hoyle, Pattern formation: an introduction to methods, 2006.
DOI : 10.1017/CBO9780511616051

K. Inoue, Computation of eigenmodes on a compact hyperbolic 3-space, Classical and Quantum Gravity, vol.16, issue.10, 1999.
DOI : 10.1088/0264-9381/16/10/304

H. Iwaniec, Spectral methods of automorphic forms, AMS Graduate Series in Mathematics. AMS Bookstore, vol.53, 2002.
DOI : 10.1090/gsm/053

S. Katok, Fuchsian Groups. Chicago Lectures in Mathematics, 1992.

R. Lehoucq, J. Weeks, J. Uzan, E. Gausmann, and J. Luminet, Eigenmodes of three-dimensional spherical spaces and their application to cosmology, Classical and Quantum Gravity, vol.19, issue.18, 2002.
DOI : 10.1088/0264-9381/19/18/305

W. Miller, Symmetry groups and their applications, 1972.

M. Moakher, A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices, SIAM Journal on Matrix Analysis and Applications, vol.26, issue.3, pp.735-747, 2005.
DOI : 10.1137/S0895479803436937

M. Pollicott, Distributions at infinity for riemann surfaces, Dynamical Systems and Ergodic Theory, pp.91-100, 1989.

F. Sausset and G. Tarjus, Periodic boundary conditions on the pseudosphere, Journal of Physics A: Mathematical and Theoretical, vol.40, issue.43, pp.12873-12899, 2007.
DOI : 10.1088/1751-8113/40/43/004
URL : https://hal.archives-ouvertes.fr/hal-00136101

C. Schmit, Quantum and classical properties of some billiards on the hyperbolic plane, Chaos and Quantum Physics, pp.335-369, 1991.
URL : https://hal.archives-ouvertes.fr/in2p3-00005026

C. Series, Some Geometrical Models of Chaotic Dynamics, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.413, issue.1844, pp.171-182, 1844.
DOI : 10.1098/rspa.1987.0108

J. P. Serre, Représentations linéaires des groupes finis, 1978.

O. Shriki, D. Hansel, and H. Sompolinsky, Rate Models for Conductance-Based Cortical Neuronal Networks, Neural Computation, vol.16, issue.8, pp.1809-1841, 2003.
DOI : 10.1016/S0006-3495(72)86068-5
URL : https://hal.archives-ouvertes.fr/hal-00173803

R. Veltz and O. Faugeras, Local/Global Analysis of the Stationary Solutions of Some Neural Field Equations, SIAM Journal on Applied Dynamical Systems, vol.9, issue.3, 2010.
DOI : 10.1137/090773611
URL : https://hal.archives-ouvertes.fr/hal-00712201

A. Weil, Groupes des formes quadratiques ind??finies et des formes bilin??aires altern??es, Séminaire Henri Cartan, vol.10, pp.1-14, 1957.
DOI : 10.1007/978-1-4757-1705-1_82
URL : http://www.numdam.org/article/SHC_1957-1958__10_1_A2_0.pdf