. Liste-des-travaux-travaux-après-la and A. Tsygvintsev, Sur l'absence d'une intégralepremì ere supplémentaire méromorphe dans leprobì eme plan des trois corps, C.R. Acad. Sci. Paris, t, vol.333, pp.125-128, 2001.

A. Tsygvintsev, Non-existence of new meromorphic first integrals in the planar three-body problem, Celestial Mechanics and Dynamical Astronomy, vol.86, issue.3, pp.237-247, 2003.
DOI : 10.1023/A:1024279320962

A. Tsygvintsev, B. D. Mestel, and A. H. Osbaldestin, Continued fractions and solutions of the Feigenbaum-Cvitanovi´cCvitanovi´c equation, C. R. Math

B. D. Mestel, A. H. Osbaldestin, and A. Tsygvintsev, Bounds on the Unstable Eigenvalue for the Asymmetric Renormalization Operator for Period Doubling, Communications in Mathematical Physics, vol.41, issue.2, pp.241-257, 2004.
DOI : 10.1007/s00220-004-1143-2

A. Tsygvintsev, On the connection between g-fractions and solutions of the Feigenbaum-Cvitanovi´cCvitanovi´c equation, Commun. Anal. Theory Contin

A. Tsygvintsev, On the convergence of continued fractions at Runckel's points. The Ramanujan Journal

H. Dullin and A. Tsygvintsev, On the analytic non-integrability of the Rattleback problem, Annales de la faculté des sciences de Toulouse
DOI : 10.5802/afst.1191

A. Tsygvintsev, On the meromorphic non-integrability of the planar three-body problem, Thèse de Doctorat, 2001.

A. Tsygvintsev, La non-intégrabilité méromorphe duprobì eme plan des trois corps, C. R. Acad. Sci. Paris Sér. I Math, vol.33, issue.3, pp.241-244, 2000.
DOI : 10.1016/s0764-4442(00)01623-2

. Tsygvintsev, On the existence of polynomial first integrals of quadratic homogeneous systems of ordinary differential equations, Journal of Physics A: Mathematical and General, vol.34, issue.11, pp.2185-2193, 2001.
DOI : 10.1088/0305-4470/34/11/311

A. Tsygvintsev, Algebraic invariant curves of plane polynomial differential systems, Journal of Physics A: Mathematical and General, vol.34, issue.3, pp.663-672, 2001.
DOI : 10.1088/0305-4470/34/3/325

A. Borisov and A. Tsygvintsev, Kovalevskaya exponents and integrable systems of classical dynamics I, II, Regular and Chaotic dynamics 1, pp.15-28, 1996.

A. Borisov and A. Tsygvintsev, Kovalevskaya's method in rigid body dynamics, Journal of Applied Mathematics and Mechanics, vol.61, issue.1, pp.27-32, 1997.
DOI : 10.1016/S0021-8928(97)00004-X

A. Tsygvintsev, Sur l'int??grabilit?? alg??brique d'un syst??me d'??quations diff??rentielles d??riv?? des ??quations d'Euler sur l'alg??bre so(4), Bulletin des Sciences Math??matiques, vol.123, issue.8, pp.665-670, 1999.
DOI : 10.1016/S0007-4497(99)00120-7

K. V. Emelyanov and A. Tsygvintsev, Kovalevskaya exponents of systems with exponential interaction, Sbornik: Mathematics, vol.191, issue.10, pp.39-50, 2000.
DOI : 10.1070/SM2000v191n10ABEH000514

. Article, J. Strelcyn, and A. Tsygvintsev, Poincaré theorems, Encyclopedia of Nonlinear Science, 2004.

G. E. Andrews, B. C. Berndt, L. Jacobson, and R. L. Lamphere, The continued fractions found in the unorganized portions of Ramanujan???s notebooks, Memoirs of the American Mathematical Society, vol.99, issue.477, 1992.
DOI : 10.1090/memo/0477

M. Audin, Intégrabilité et non-intégrabilité de systèmes hamiltoniens, 2000.

N. Aronszajn, W. Donoghue, and . Jr, On exponential representations of analytic functions in the upper half-plane with positive imaginary part, Journal d'Analyse Math??matique, vol.60, issue.69, pp.113-127, 1964.
DOI : 10.1007/BF02937349

A. Audin, Les systèmes hamiltoniens et leur intégrabilité, 2000.

F. S. Acton, Numerical Methods that Work. 2nd printing, Math. Assoc. Amer, 1990.

A. Arneodo, P. Coullet, and C. Tresser, A renormalization group with periodic behaviour, Physics Letters A, vol.70, issue.2, pp.74-76, 1979.
DOI : 10.1016/0375-9601(79)90027-6

V. I. Arnold and A. L. Krylov, Uniform distribution of points on a sphere and certain ergodic properties of solutions of linear ordinary differential equations in a complex domain, Dokl. Akad. Nauk SSSR, vol.148, pp.1963-1972

K. M. Briggs, T. W. Dixon, and G. Szekeres, Analytic Solutions of the Cvitanovi?????Feigenbaum and Feigenbaum???Kadanoff???Shenker Equations, International Journal of Bifurcation and Chaos, vol.08, issue.02, pp.347-357, 1998.
DOI : 10.1142/S0218127498000206

S. V. Bolotin, Condition for nonintegrability in the sense of Liouville of Hamiltonian systems, Vestnik Moskov. Univ. Ser. I Mat. Mekh, issue.3, pp.58-64, 1986.

A. V. Borisov and I. S. Mamaev, Strange attractors in rattleback dynamics, Physics-Uspekhi, vol.46, issue.4, pp.393-403, 2003.
DOI : 10.1070/PU2003v046n04ABEH001306

H. Bruns, Ueberdie Integrale des vierkörper Problems, Acta Math, pp.25-961887

A. Beardon, Continued fractions, discrete groups and complex dynamics , Computational Methods and Function Theory, pp.535-594, 2001.

D. Boucher, Sur la non-intégrabilité duprobì eme plan des trois corps de masseségalesmasseségales, C. R. Acad. Sci. Paris Sér. I Math, p.331, 2000.
DOI : 10.1016/s0764-4442(00)01666-9

A. ;. Chenciner, J. Gerver, . Montgomery, . Richard, and . Simó, Carles Simple choreographic motions of N bodies: a preliminary study. Geometry , mechanics, and dynamics, pp.287-308, 2002.

P. Collet, J. Eckmann, O. E. Lanford, and . Iii, Universal properties of maps on an interval, Communications in Mathematical Physics, vol.54, issue.3, pp.211-254, 1980.
DOI : 10.1007/BF02193555

P. Coullet and C. Tresser, IT??RATIONS D'ENDOMORPHISMES ET GROUPE DE RENORMALISATION, Le Journal de Physique Colloques, vol.39, issue.C5, pp.25-28, 1978.
DOI : 10.1051/jphyscol:1978513

J. Christensen, . Peter-reus, and P. Fischer, Linear independence of iterates and meromorphic solutions of functional equations, Proc. Amer, pp.1137-1143, 1994.
DOI : 10.1090/S0002-9939-1994-1182697-1

J. Chazy, Sur l'allure du mouvement dans le probl??me des trois corps quand le temps cro??t ind??finiment, Annales scientifiques de l'??cole normale sup??rieure, vol.39, pp.29-130, 1922.
DOI : 10.24033/asens.739
URL : http://archive.numdam.org/article/ASENS_1922_3_39__29_0.pdf

R. Cushman, Examples of nonintegrable analytic Hamiltonian vector fields with no small divisors, Transactions of the American Mathematical Society, vol.238, pp.45-55, 1978.
DOI : 10.1090/S0002-9947-1978-0478223-8

W. F. Donoghue and . Jr, Monotone matrix functions and analytic continuation, Die Grundlehren der mathematischen Wissenschaften, 1974.

J. Eckmann and H. Epstein, Bounds on the unstable eigenvalue for period doubling, Communications in Mathematical Physics, vol.3, issue.1, pp.427-435, 1990.
DOI : 10.1007/BF02108789

J. Eckmann and H. Epstein, On the existence of fixed points of the composition operator for circle maps, Communications in Mathematical Physics, vol.8, issue.2, pp.213-231, 1986.
DOI : 10.1007/BF01209392

H. Epstein and J. Lascoux, Analyticity properties of the Feigenbaum function, Communications in Mathematical Physics, vol.77, issue.3, pp.437-453, 1981.
DOI : 10.1007/BF01209078

H. Epstein, New proofs of the existence of the Feigenbaum functions, Communications in Mathematical Physics, vol.39, issue.99, pp.395-426, 1986.
DOI : 10.1007/BF01207254

H. Epstein, Fixed Points of Composition Operators, 1988.
DOI : 10.1007/978-1-4613-1017-4_6

H. Epstein, Existence and Properties of p-tupling Fixed Points, Communications in Mathematical Physics, vol.215, issue.2, pp.443-476, 2000.
DOI : 10.1007/s002200000311

N. P. Erugin, The method of Lappo-Danilevskii in the theory of linear differential equations, Izdat. Leningr. Univ, 1956.

K. V. Emelyanov, On the classification problem for Birkhoff integrable systems with potentials of exponential type, Mathematical Notes, vol.51, issue.2, pp.797-800, 2000.
DOI : 10.1007/BF02676341

M. J. Feigenbaum, Quantitative universality for a class of nonlinear transformations, Journal of Statistical Physics, vol.54, issue.1, pp.25-52, 1978.
DOI : 10.1007/BF01020332

M. J. Feigenbaum, L. P. Kadanoff, and S. J. Shenker, Quasiperiodicity in dissipative systems: A renormalization group analysis, Physica D: Nonlinear Phenomena, vol.5, issue.2-3, pp.370-386, 1982.
DOI : 10.1016/0167-2789(82)90030-6

A. Fomenko, Integrability and Nonintegrability in Geometry and Mechanics, 1988.
DOI : 10.1007/978-94-009-3069-8

L. Fuchs, Zur Theorie der linearen Differentialgleichungen mit veränderlichen Coefficienten, pp.11-158, 1865.

F. Gantmacher, The theory of matrices, 1998.

A. Garcia and M. Hubbard, Spin Reversal of the Rattleback: Theory and Experiment, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.418, issue.1854, pp.165-197, 1988.
DOI : 10.1098/rspa.1988.0078

C. F. Gauss, Disguisitiones generales circa seriem infinitam, Dars prior, Comm. Soc. reg. Gött, vol.11, issue.111, pp.123-162

F. Gesztesy and B. Simon, On the determination of a potential from three spectra, Advances in Mathematical Sciences, pp.85-92, 1999.
DOI : 10.1090/trans2/189/07

J. Gill, Infinite compositions of Möbius transformations, Trans. Amer. Math. Soc, vol.176, pp.479-487, 1973.

A. A. Glutsyuk, On convergence of generalized continued fractions and Ramanujan's conjecture, Comptes Rendus Mathematique, vol.341, issue.7, pp.427-432, 2005.
DOI : 10.1016/j.crma.2005.08.001

A. Goriely, A brief history of Kovalevskaya exponents and modern developments , Regular and Chaotic Dynamics: Special Kovalevskaya Edi- tion

J. Gray, Linear differential equations and group theory from Riemann to Poincaré, 1986.

L. Jacobsen, General convergence of continued fractions, Transactions of the American Mathematical Society, vol.294, issue.2, pp.477-485, 1986.
DOI : 10.1090/S0002-9947-1986-0825716-1

E. Julliard-tosel, Non-intégrabilité algébrique et méromorphe de probì eme de N corps, 2000.

E. Julliard-tosel, Bruns' theorem: The proof and some generalizations, Celestial Mechanics and Dynamical Astronomy, vol.76, issue.4, pp.241-281, 2000.
DOI : 10.1023/A:1008346516349

E. Julliard-tosel, Un nouveau crit??re de non-int??grabilit?? m??romorphe d'un Hamiltonien, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.330, issue.12, pp.1097-1102, 2000.
DOI : 10.1016/S0764-4442(00)00320-7

E. Julliard-tosel, Un résultat de non-intégrabilité pour le potentiel en 1/r 2 . (A non-integrability result for the inverse square potential)

R. V. Jensen and L. K. Ma, Nonuniversal behavior of asymmetric unimodal maps, Physical Review A, vol.31, issue.6, pp.3993-3995, 1985.
DOI : 10.1103/PhysRevA.31.3993

M. G. Krein and M. A. Rutman, Linear operators leaving invariant a cone in a Banach space English Translation: Functional analysis and measure theory, Usp. Mat. Nauk, vol.3, issue.1, pp.3-95, 1948.

K. Khanin and E. Vul, Circle homeomorphisms with weak discontinuities, Adv. Soviet Math, vol.3, pp.57-98, 1991.

V. V. Kozlov, Topological obstacles to the integrability of natural mechanical systems, Dokl. Akad. Nauk SSSR, vol.249, issue.6, pp.1299-1302, 1979.

V. V. Kozlov, Symmetry groups of dynamical systems. (Russian) Prikl, Mat. Mekh. J. Appl. Math. Mech, vol.52, issue.52 4, pp.531-541, 1988.

V. V. Kozlov, Splitting of the separatrices in the perturbed Euler- Poinsot problem, Vestnik Moskov. Univ. Ser. I Mat. Meh, vol.31, issue.6, pp.99-104, 1976.

V. V. Kozlov and D. V. Treshchëv, Nonintegrability of the general problem of rotation of a dynamically symmetric heavy rigid body with a fixed point. I. Vestnik Moskov, Univ. Ser. I Mat. Mekh, issue.6, pp.73-81, 1985.

V. V. Kozlov, Solution branching and polynomial integrals in an invertible system on a torus, Mathematical Notes of the Academy of Sciences of the USSR, vol.16, issue.No. 3, pp.100-104, 1988.
DOI : 10.1007/BF01158121

V. V. Kozlov, Tensor invariants of quasihomogeneous systems of differential equations, and the Kovalevskaya-Lyapunov asymptotic method, Mathematical Notes, vol.31, issue.No. 4, pp.46-52, 1992.
DOI : 10.1007/BF02102118

V. V. Kozlov and . Symmetry, Topology and Resonances in Hamiltonian Mechanics, 1996.

V. V. Kozlov and D. V. Treshchëv, Kovalevskaya numbers of generalized toda chains, Mathematical Notes of the Academy of Sciences of the USSR, vol.31, issue.No. 4, pp.17-28, 1989.
DOI : 10.1007/BF01139615

O. E. Lanford, A computer-assisted proof of the Feigenbaum conjectures, Bulletin of the American Mathematical Society, vol.6, issue.3, pp.427-434, 1982.
DOI : 10.1090/S0273-0979-1982-15008-X

S. Marmi, Chaotic behaviour in the Solar System (following J. Laskar), Séminaire Bourbaki n, pp.113-136, 2000.

B. Malgrange, ON NONLINEAR DIFFERENTIAL GALOIS THEORY, Chinese Ann. Math. Ser. B, vol.23, issue.2, pp.219-226, 2002.
DOI : 10.1142/9789812562265_0013

C. T. Mcmullen, Renormalization and 3-Manifolds which Fiber over the Circle, Annals of Mathematical Studies, vol.142, 1996.
DOI : 10.1515/9781400865178

B. D. Mestel and A. H. Osbaldestin, Feigenbaum theory for unimodal maps with asymmetric critical point, Journal of Physics A: Mathematical and General, vol.31, issue.14, pp.3287-3296, 1998.
DOI : 10.1088/0305-4470/31/14/014

B. D. Mestel and A. H. Osbaldestin, Feigenbaum Theory for Unimodal Maps with Asymmetric Critical Point: Rigorous Results, Communications in Mathematical Physics, vol.197, issue.1, pp.211-228, 1998.
DOI : 10.1007/s002200050448

B. Mestel and A. Osbaldestin, Renormalisation in implicit complex maps, Physica D: Nonlinear Phenomena, vol.39, issue.2-3, pp.149-162, 1989.
DOI : 10.1016/0167-2789(89)90001-8

J. Morales-ruiz, Differential Galois theory and non?integrability of Hamiltonian systems, 1999.
DOI : 10.1007/978-3-0348-0723-4

J. J. Morales-ruiz, J. Ramis, and . Pierre, Galoisian obstructions to integrability of Hamiltonian systems, Methods and Applications of Analysis, vol.8, issue.1, pp.509-513, 1995.
DOI : 10.4310/MAA.2001.v8.n1.a3

B. D. Mestel and A. H. Osbaldestin, Asymptotics of scaling parameters for period-doubling in unimodal maps with asymmetric critical points, Journal of Mathematical Physics, vol.41, issue.7
DOI : 10.1063/1.533398

I. Newton, Les principes mathématique de la philosophie naturelle, 1985.

K. Sundman, M??moire sur le probl??me des trois corps, Acta Mathematica, vol.36, issue.0, pp.105-107, 1913.
DOI : 10.1007/BF02422379

S. Ostlund, J. Rand, E. Sethna, and . Siggia, Universal properties of the transition from quasi-periodicity to chaos in dissipative systems, Physica D: Nonlinear Phenomena, vol.8, issue.3, pp.303-342, 1983.
DOI : 10.1016/0167-2789(83)90229-4

H. Poincaré, Sur les fonctions Fuchsiennes, C. R, vol.92, pp.333-335, 1881.

H. Poincaré, Les méthodes novelles de la mécanique céleste, 1892.

P. Painlevé, Mémoire sur les intégrales premiéres duprobì eme des n corps, Acta Math. Bull. Astr. T, vol.15, 1898.

D. Bedford and J. Swift, Universality and renormalisation in dynamical systems, CUP, 1989.

H. Runckel, Bounded analytic functions in the unit disk and the behavior of certain analytic continued fractions near the singular line, J. reine angew. Math, vol.281, pp.97-125, 1976.

B. Rimeann, Grundalgenfüreine allgemeine Theorie der Functionen einer veränderlichenver¨veränderlichen complexen Grösse, Inagural dissertation, pp.3-45, 1851.

S. Shenker, Scaling behavior in a map of a circle onto itself: Empirical results, Physica D: Nonlinear Phenomena, vol.5, issue.2-3, pp.405-411, 1982.
DOI : 10.1016/0167-2789(82)90033-1

T. J. Stieltjes, Recherches sur les fractions continues, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.8, issue.4, pp.1-1221, 1894.
DOI : 10.5802/afst.108
URL : http://archive.numdam.org/article/AFST_1995_6_4_2_J36_0.pdf

A. J. Maciejewski and . Strelcyn, On the algebraic non-integrability of Halphen system, Physics Letters A, vol.201, issue.2-3, pp.161-166, 1995.
DOI : 10.1016/0375-9601(95)00285-B

D. Sullivan, Bounds, quadratic differentials and renormalization conjectures In: Mathematics into the Twenty-first Century, 1992.

K. F. Sundman, M??moire sur le probl??me des trois corps, Acta Mathematica, vol.36, issue.0, pp.105-179, 1912.
DOI : 10.1007/BF02422379

I. A. Ta?-imanov, Topological obstructions to the integrability of geodesic flows on nonsimply connected manifolds, Izv. Akad. Nauk SSSR Ser. Mat, vol.51, issue.2, pp.429-435, 1987.

I. A. Ta?-imanov, Topological properties of integrable geodesic flows, Russian) Mat. Zametki, pp.283-284, 1988.

G. Teschl, Jacobi operators and completely integrable nonlinear lattices, Mathematical Surveys and Monographs, 72, 2000.
DOI : 10.1090/surv/072
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.298.9029

E. B. Van-vleck, On the convergence of algebraic continued fractions whose coefficients have limiting values, Transactions of the American Mathematical Society, vol.5, issue.3, pp.253-262, 1904.
DOI : 10.1090/S0002-9947-1904-1500672-9

E. V. Van-vleck, On the Convergence of the Continued Fraction of Gauss and Other Continued Fractions, The Annals of Mathematics, vol.3, issue.1/4, pp.1-18, 1901.
DOI : 10.2307/1967627

H. Wall, Analytic theory of continued fractions, D. van Nostrand Company Inc, 1948.

E. T. Whittaker, A Treatise on the Analytical Dynamics of particles and Rigid Bodies, 1970.
DOI : 10.1017/CBO9780511608797

A. Wintner, The analytical foundations of Celestial Mechanics, 1941.

H. Yoshida, Necessary condition for existence of algebraic first integrals , Celestial Mechanics. 1983.V. 31, pp.363-399

S. Ziglin, Branching of solutions and non-existence of first integrals in Hamiltonian Mechanics I, Funct, Anal. Appl, vol.16, pp.181-189, 1982.

S. L. Ziglin, On the absence of a real-analytic first integral for ABC flow when A=B, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.8, issue.1, pp.272-273, 1998.
DOI : 10.1063/1.166305