@article{AIHPA_1992__56_4_375_0, author = {Cicogna, G. and Gaeta, G.}, title = {Lie-point symmetries in bifurcation problems}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {375--414}, publisher = {Gauthier-Villars}, volume = {56}, number = {4}, year = {1992}, mrnumber = {1175476}, zbl = {0812.34032}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1992__56_4_375_0/} }
Cicogna, G.; Gaeta, G. Lie-point symmetries in bifurcation problems. Annales de l'I.H.P. Physique théorique, Tome 56 (1992) no. 4, pp. 375-414. http://www.numdam.org/item/AIHPA_1992__56_4_375_0/
[Arn] Geometrical Methods in the Theory of Ordinary Differential Equations, Springer, Berlin, 1983. | MR
,[BC] Similarity Methods for Differential Equations, Springer, New York, 1974. | MR | Zbl
and ,[BK] Symmetries and Differential Equations, Springer, New York, 1989. | MR | Zbl
and ,[CH] Methods of Bifurcation Theory, Springer, New York, 1982. | MR | Zbl
and ,[CHW] The Computer Calculation of Lie Point Symmetries of Large Systems of Differential Equations, Preprint CRM-1689, Montreal, 1990. | MR
, and ,[Cic] A Nonlinear Version of the Equivariant Bifurcation Lemma, J. Phys. A, Vol. 23, 1990, p. L1339. | MR | Zbl
,[CG86] Spontaneous Linearization and Periodic Solutions in Hopf and Symmetric Bifurcations, Phys. Lett. A, Vol. 116, 1986, p. 303. | MR
and ,[CG90] Lie-Point Symmetries and Poincare' Normal Forms for Dynamical Systems, J. Phys. A., Vol. 23, 1990, p. L799; see also: Lie-Point Symmetries for Autonomous Symmetries and Resonance, Preprint 1991, to appear in J. Phys. A. | MR | Zbl
and ,[CK] Symmetry and Symmetry-Breaking Bifurcations in Fluid Dynamics, Ann. Rev. Fluid Mech, Vol. 23, 1991, p. 341. | MR | Zbl
and ,[Cra] Boundary Conditions as Symmetry Constraints, in Singularity Theory and its Applications, Warwick, 1989, R. M. ROBERTS and I. STEWART Eds., Lecture Notes Math., No. 1463, Springer, Berlin, 1991. | MR | Zbl
, , , and ,[Ehr] Les prolongements d'une variété différentiable, I-V, C. R. Acad. Sci. Paris: I. Calcul des jets, prolongement principal, 233, 1951, p.598; II. L'espace des jets d'ordre r de Vn dans Vm, 233, 1951, p. 777; III. Transitivité des prolongements, 233, 1951, p. 1081; IV. Éléments de contact et éléments d'enveloppe, 234, 1952, p. 1028; V. Covariants différentiels et prolongements d'une structure infinitésimale, 234, 1952, p. 1424; Structures locales et structures infinitésimales, 234, 1952, p.587; Extension du calcul des jets aux jets non holonomes, 239, 1954, p. 1762; Applications de la notion de jet non holonome, 240, 1955, p. 397; Les prolongements d'un espace fibré différentiable, 240, 1955, p. 1755. Les prolongements d'une variété différentiable, Atti del IV congresso dell'Unione Matematica Italiana, 1951. | MR | Zbl
,[Elp] A Simple Global Characterization for Normal Forms of Singular Vector Fields, Physica D, Vol. 29, 1987, p. 95. | MR | Zbl
, , , and ,[Gae] Bifurcation Theory and Nonlinear Symmetry, Nonlinear Analysis, Vol. 17, 1991, p. 825. | Zbl
,[Gae90a] Bifurcation and Symmetry Breaking, Phys. Rep., Vol. 189, 1990, p. 1. | MR
,[Gae90b] Lie Point Symmetries and Periodic Solutions for Autonomous ODE, Preprint, C. P. Th., Palaiseau, 1990; Autonomous Dynamical Systems, LPTI Symmetries, Topology of Trajectories, and Periodic Solutions; Preprint, C. P. Th., Palaiseau, 1991.
,[Gae91] Michel Theorem and Critical Sections of Gauge Functionals, Preprint, C. P. Th., Palaiseau, 1991.
,[GMS] Bifurcation Problems with Hidden Symmetry, in Partial Differential Equations and Dynamical Systems, W. E. FITZGIBBON Ed., Res. Notes Math., Vol. 101, Pitman, Boston, 1984. | Zbl
, and ,[GG] Stable Mappings and Their Singularities, Springer, New York, 1973. | MR | Zbl
and ,[GS] Hopf Bifurcation in the Presence of Symmetry, Arch. Rat. Mech. Anal., Vol. 87, 1985, p. 107. | MR | Zbl
and ,[GSS] Singularity and Groups in Bifurcation Theory, Vol. II, Springer, New York, 1988. | Zbl
, and ,[GH] Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields, Springer, New York, 1983. | MR | Zbl
and ,[HPS] Invariant Manifolds, Lecture Notes in Mathematics, No. 583, Springer, New York, 1975. | MR | Zbl
, and ,[IJ] Elementary Stability and Bifurcation Theory, Springer, Berlin, 1981; second edition, 1990. | MR | Zbl
and ,[JS] Bifurcating Time Periodic Solutions and Their Stability, Arch. Rat. Mech. Anal., Vol. 45, 1972, p. 75. | MR | Zbl
and ,[MM] J. E. MARSDEN and M. MCCRACKEN Eds., The Hopf Bifurcation and its Applications, Springer, New York, 1976. | MR | Zbl
[Olv] Applications of Lie Groups to Differential Equations, Springer, Berlin, 1986. | MR | Zbl
,[Ovs] Group Properties of Differential Equations (in russian), Novosibirsk, 1962, Group Analysis of Differential Equations, Academic Press, New York, 1982. | MR
,[Rue73] Bifurcations in the Presence of a Symmetry Group, Arch. Rat. Mech. Anal., Vol. 51, 1973, p. 136. | MR | Zbl
,[Rue89] Elements of Differentiable Dynamics and Bifurcation Theory, Academic Press, London, 1989. | MR | Zbl
,[Sat73] Topics in Stability and Bifurcation Theory, Lect. Notes Math., No. 309, Springer, Berlin, 1973. | MR | Zbl
,[Sat79] Group Theoretic Methods in Bifurcation Theory, Lect. Notes Math., No. 762, Springer, Berlin, 1979. | MR | Zbl
,[Sat83] Branching in the Presence of Symmetry, S.I.A.M., Philadelphia, 1983. | MR | Zbl
,[SW] Lie Groups and Algebras, Springer, New York, 1986. | MR | Zbl
and ,[Van] Local Bifurcation and Symmetry, Pitman, Boston, 1982. | MR | Zbl
,[Vin84] Local Symmetries and Conservation Laws, Acta Appl. Math., Vol. 2, 1984, p. 21. | MR | Zbl
,[Vin89] Symmetries and Conservation Laws of Partial Differential Equations: Basic Notions and Results, Acta Appl. Math., Vol. 15, 1989, p. 3. | MR | Zbl
,[Win] Group Theory and Exact Solutions of Partially Integrable Differential Systems, in: Partially Integrable Evolution Equations in Physics, R. CONTE and N. BOCCARA Eds., Kluwer, 1990. | MR | Zbl
,[Wul] Limit Cycles as Invariant Functions of Lie Groups, J. Phys. A, Vol. 12, 1979, p. L73. | MR | Zbl
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