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

T. I. Baker and J. D. Cowan, Spontaneous pattern formation and pinning in the primary visual cortex, Journal of Physiology-Paris, vol.103, issue.1-2, pp.52-68, 2009.
DOI : 10.1016/j.jphysparis.2009.05.011

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

R. Ben-yishai, R. Bar-or, and H. Sompolinsky, Theory of orientation tuning in visual cortex., Proceedings of the National Academy of Sciences, pp.3844-3848, 1995.
DOI : 10.1073/pnas.92.9.3844

J. Bigun and G. Granlund, Optimal orientation detection of linear symmetry, Proc. First Int'l Conf. Comput. Vision, pp.433-438, 1987.

B. Blumenfeld, D. Bibitchkov, and M. Tsodyks, Neural network model of the primary visual cortex: From functional architecture to lateral connectivity and back, Journal of Computational Neuroscience, vol.16, issue.2, pp.219-241, 2006.
DOI : 10.1007/s10827-006-6307-y

I. Bosch-vivancos and P. , Chossat and I. Melbourne New planforms in systems of partial differential equations with Euclidean symmetry Archive for rational mechanics and analysis, pp.199-224, 1995.

W. H. Bosking, Y. Zhang, B. Schofield, and D. Fitzpatrick, Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex, The Journal of Neuroscience, vol.17, issue.6, pp.2112-2127, 1997.

P. C. Bressloff and J. D. Cowan, The functional geometry of local and horizontal connections in a model of V1, Journal of Physiology-Paris, vol.97, issue.2-3, pp.221-236, 2003.
DOI : 10.1016/j.jphysparis.2003.09.017

P. C. Bressloff and J. D. Cowan, A spherical model for orientation and spatial-frequency tuning in a cortical hypercolumn, Philosophical Transactions of the Royal Society B: Biological Sciences, vol.358, issue.1438, 2003.
DOI : 10.1098/rstb.2002.1109

P. C. Bressloff, Spatially periodic modulation of cortical patterns by long-range horizontal connections, Physica D: Nonlinear Phenomena, vol.185, issue.3-4, pp.131-157, 2003.
DOI : 10.1016/S0167-2789(03)00238-0

P. C. Bressloff and J. D. Cowan, The visual cortex as a crystal, Physica D: Nonlinear Phenomena, vol.173, issue.3-4, pp.3-4226, 2002.
DOI : 10.1016/S0167-2789(02)00677-2

P. C. Bressloff, J. D. Cowan, M. Golubitsky, and P. J. Thomas, Scalar and pseudoscalar bifurcations motivated by pattern formation on the visual cortex, Nonlinearity, vol.14, issue.4, p.739, 2001.
DOI : 10.1088/0951-7715/14/4/305

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 and A. M. Oster, Theory for the alignment of cortical feature maps during development, Physical Review E, vol.82, issue.2, p.21920, 2010.
DOI : 10.1103/PhysRevE.82.021920

S. Chemla and F. Chavane, Voltage-sensitive dye imaging: Technique review and models, Journal of Physiology-Paris, vol.104, issue.1-2, pp.40-50, 2010.
DOI : 10.1016/j.jphysparis.2009.11.009

P. Chossat, G. Faye, and O. Faugeras, Bifurcation of Hyperbolic Planforms, Journal of Nonlinear Science, vol.10, issue.8, 2011.
DOI : 10.1007/s00332-010-9089-3

URL : https://hal.archives-ouvertes.fr/hal-00807355

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

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

G. Citti and A. Sarti, A Cortical Based Model of Perceptual Completion in the Roto-Translation Space, Journal of Mathematical Imaging and Vision, vol.11, issue.3, pp.307-326, 2006.
DOI : 10.1007/s10851-005-3630-2

D. P. Edwards, K. P. Purpura, and E. Kaplan, Contrast sensitivity and spatial frequency response of primate cortical neurons in and around the cytochrome oxidase blobs, Vision Research, vol.35, issue.11, pp.1501-1523, 1995.
DOI : 10.1016/0042-6989(94)00253-I

I. Erdélyi, Higher Transcendental Functions, 1985.

G. Ermentrout and J. Cowan, A mathematical theory of visual hallucination patterns, Biological Cybernetics, vol.135, issue.Suppl. 247, pp.137-150, 1979.
DOI : 10.1007/BF00336965

G. Faye and P. Chossat, Bifurcation Diagrams and Heteroclinic Networks of Octagonal H-Planforms, Journal of Nonlinear Science, vol.13, issue.2, pp.277-326, 2012.
DOI : 10.1007/s00332-011-9118-x

URL : https://hal.archives-ouvertes.fr/hal-00807364

G. Faye, P. Chossat, and O. Faugeras, Analysis of a hyperbolic geometric model for visual texture perception, The Journal of Mathematical Neuroscience, vol.1, issue.1, 2011.
DOI : 10.1137/090773611

URL : https://hal.archives-ouvertes.fr/hal-00784424

M. Golubitsky, L. J. Shiau, and A. Török, Bifurcation on the Visual Cortex with Weakly Anisotropic Lateral Coupling, SIAM Journal on Applied Dynamical Systems, vol.2, issue.2, pp.97-143, 2003.
DOI : 10.1137/S1111111102409882

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

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

M. Haragus, G. Iooss, and E. Sci, Local bifurcations, center manifolds, and normal forms in infinite dimensional systems, 2010.
DOI : 10.1007/978-0-85729-112-7

URL : https://hal.archives-ouvertes.fr/hal-00877080

S. Helgason, Groups and Geometric Analysis, Mathematical Surveys and Monographs, vol.83, 2000.
DOI : 10.1090/surv/083

R. B. Hoyle, Pattern Formation: an Introduction to Methods, 2006.
DOI : 10.1017/CBO9780511616051

D. H. Hubel and T. N. , Receptive fields and functional architecture in two nonstriate visual areas (18 and 19) of the cat, Journal of Neurophysiology, vol.28, pp.229-289, 1965.

D. H. Hubel and T. N. , Receptive fields and functional architecture of monkey striate cortex, The Journal of Physiology, vol.195, issue.1, p.215, 1968.
DOI : 10.1113/jphysiol.1968.sp008455

D. H. Hubel and T. N. , Functional architecture of macaque monkey, Proceedings of the Royal Society, pp.1-59, 1977.

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

M. Kaschube, M. Schnabel, S. Löwel, D. M. Coppola, L. E. White et al., Universality in the Evolution of Orientation Columns in the Visual Cortex, Science, vol.330, issue.6007, p.3301113, 2010.
DOI : 10.1126/science.1194869

M. Kaschube, M. Schnabel, and F. Wolf, Self-organization and the selection of pinwheel density in visual cortical development, New Journal of Physics, vol.10, issue.1, p.15009, 2008.
DOI : 10.1088/1367-2630/10/1/015009

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

H. Kluver, Mescal, and mechanisms of hallucinations, 1966.

H. Knutsson, Representing Local Structure Using Tensors II, Scandinavian Conference on Image Analysis, pp.244-251, 1989.
DOI : 10.1007/978-3-540-75757-3_110

P. S. Leon, I. Vanzetta, G. S. Masson, and L. U. Perrinet, Motion clouds: model-based stimulus synthesis of natural-like random textures for the study of motion perception, Journal of Neurophysiology, vol.107, issue.11, pp.3217-3220
DOI : 10.1152/jn.00737.2011

URL : https://hal.archives-ouvertes.fr/hal-00726828

M. S. Livingstone and D. H. Hubel, Anatomy and physiology of a color system in the primate visual cortex, Journal of Neuroscience, vol.4, pp.309-356, 1984.

J. S. Lund, A. Angelucci, and P. C. Bressloff, Anatomical Substrates for Functional Columns in Macaque Monkey Primary Visual Cortex, Cerebral Cortex, vol.13, issue.1, pp.15-24, 2003.
DOI : 10.1093/cercor/13.1.15

I. Melbourne, A singularity theory analysis of bifurcation problems with octahedral symmetry, Dynamics and Stability of Systems, vol.56, issue.4, 1986.
DOI : 10.1016/0040-9383(75)90036-1

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

J. D. Murray, Mathematical Biology II, Spatial Models and Biomedical Applications, 2003.

G. A. Orban, H. Kennedy, and J. Bullier, Velocity sensitivity and direction selectivity of neurons in areas V1 and V2 of the monkey: influence of eccentricity, Journal of Neurophysiology, vol.56, issue.2, pp.462-480, 1986.

G. Oster, Phosphenes, Scientific American, vol.222, issue.2, p.82, 1970.
DOI : 10.1038/scientificamerican0270-82

A. M. Oster and P. C. Bressloff, A Developmental Model of Ocular Dominance Column Formation on a Growing Cortex, Bulletin of Mathematical Biology, vol.237, issue.1, 1007.
DOI : 10.1007/s11538-005-9055-7

J. Petitot, The neurogeometry of pinwheels as a sub-Riemannian contact structure, Journal of Physiology-Paris, vol.97, issue.2-3, pp.265-309, 2003.
DOI : 10.1016/j.jphysparis.2003.10.010

J. Petitot, Neurogéométrie de la Vision, 2009.

G. Sanguinetti, A. Sarti, and G. Citti, Implementation of a Model for Perceptual Completion in R 2??S 1, Communications in Computer and Information Science, vol.24, pp.188-201, 2009.
DOI : 10.1007/978-3-642-10226-4_15

A. Sarti and G. Citti, Non-commutative field theory in the visual cortex Computer Vision: from surfaces to 3D objects, 2010.

A. Sarti, G. Citti, and J. Petitot, The symplectic structure of the primary visual cortex, Biological Cybernetics, vol.6, issue.4, pp.33-48, 2008.
DOI : 10.1007/s00422-007-0194-9

J. Schummers, J. Mariño, and M. Sur, Synaptic Integration by V1 Neurons Depends on Location within the Orientation Map, Neuron, vol.36, issue.5, pp.969-978, 2002.
DOI : 10.1016/S0896-6273(02)01012-7

J. P. Serre-hermann, Représentations Linéaires des Groupes Finis, 1978.

L. C. Sincich and J. C. Horton, Divided by Cytochrome Oxidase: A Map of the Projections from V1 to V2 in Macaques, Science, vol.295, issue.5560, pp.1734-1737, 2002.
DOI : 10.1126/science.1067902

A. Terras, Harmonic analysis on symmetric spaces and applications, 1988.
DOI : 10.1007/978-1-4612-5128-6

R. B. Tootell, S. L. Hamilton, M. S. Silverman, E. Switkes, R. L. De et al., Functional anatomy of macaque striate cortex. V. Spatial Frequency, Journal of Neuroscience, vol.8, pp.1610-1624, 1988.

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

R. Veltz and O. Faugeras, Illusions in the ring model of visual orientation selectivity, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00846138

G. N. Watson, A Treatise on the Theory of Bessel Functions, The Mathematical Gazette, vol.18, issue.231, 1995.
DOI : 10.2307/3605513

H. R. Wilson and J. D. Cowan, Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons, Biophysical Journal, vol.12, issue.1, pp.1-24, 1972.
DOI : 10.1016/S0006-3495(72)86068-5

H. R. Wilson and J. D. Cowan, A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue, Kybernetik, vol.12, issue.2, pp.55-80, 1973.
DOI : 10.1007/BF00288786

F. Wolf and T. Geisel, Spontaneous pinwheel annihilation during visual development, Nature, vol.395, issue.6697, pp.73-78, 1998.
DOI : 10.1038/25736