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Persistent properties of bifurcations. (English) Zbl 1194.37001
Summary: We review results about bifurcations which occur in families of differential equations. Persistent properties are defined to be those which remain when the family of equations is perturbed. We provide a list of such properties which is relevant for numerical studies of dynamical systems.

MSC:
37-01Instructional exposition (dynamical systems and ergodic theory)
37GxxLocal and nonlocal bifurcation theory
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References:
[1] Arnold, V. I.: Loss of stability of self oscillations close to resonance and versal deformations of equivariant vector fields. Funct. anal. Appl. 11, 85-92 (1977) · Zbl 0411.58013
[2] Feigenbaum, M. J.: Quantitative universality for a class of nonlinear transformations. J. stat. Phys. 19, 25-52 (1978) · Zbl 0509.58037
[3] Gollub, J. P.; Benson, S. V.: Many routes to turbulent convection. J. fluid mech. 100, 449-470 (1980)
[4] Gollub, J. P.; Swinney, H.: Onset of turbulence in rotating fluid. Physical review letters 35, 927-930 (1975)
[5] Guckenheimer, J.: M.m.peixotoone-parameter families of vector fields on two-manifolds: another nondensity theorem in dynamical systems. One-parameter families of vector fields on two-manifolds: another nondensity theorem in dynamical systems, 111-128 (1973) · Zbl 0285.58007
[6] Guckenheimer, J.: Lectures on bifurcation theory, dynamical systems. CIME lectures 1978 (1980) · Zbl 0451.58025
[7] Guckenheimer, J.; Holmes, P.: Nonlinear oscillations, dynamical systems, and bifurcation theory. (1983) · Zbl 0515.34001
[8] Hénon, M.: A two-dimensional mapping with a strange attractor. Comm. math. Phys. 50, 69-78 (1976) · Zbl 0576.58018
[9] Herman, M.: Mesure de Lebesgue et nombre de rotation. Lecture notes in math. 597, 271-293 (1977)
[10] Herman, M.: Sur la conjugaison differentiable des diffeomorphismes du circle a des rotations. Publ. I.H.E.S. 49, 5-234 (1979)
[11] Hirsch, M.; Pugh, C.; Shub, M.: Invariant manifolds. Lecture notes in mathematics 583 (1977)
[12] Libchaber, A.; Maurer, J.: A Rayleigh-Bénard experiment: helium in a small box. (April 1981)
[13] Marsden, J.; Mccracken, M.: The Hopf bifurcation and its applications. (1976) · Zbl 0346.58007
[14] Newhouse, S. E.: The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms. Publ. I.H.E.S. 50, 101-151 (1979) · Zbl 0445.58022
[15] Newhouse, S. E.; Palis, J.; Takens, F.: Stable arcs of diffeomorphisms. Bull. am. Math. soc. 82, 499-502 (1976) · Zbl 0339.58008
[16] Pomeau, Y.; Manneville, P.: Intermittent transition to turbulence in dissipative dynamical systems. Comm. math. Phys. 75, 189-197 (1980)
[17] D. Rand, Dynamics and symmetry, Predictions for modulated waves in rotating fluids, Arch. Rat. Mech. Anal., to appear. · Zbl 0495.76031
[18] Ruelle, D.; Takens, F.: On the nature of turbulence. Comm. math. Phys. 20, 167-192 (1971) · Zbl 0223.76041
[19] Sil’nikov, L. P.: A contribution to the problem of the structure of an extended neighborhood of a structurally stable equilibrium of saddle-focus type. Math. USSR sb. 10, 91-102 (1970)
[20] Smale, S.: Diffeomorphisms with many periodic points. Differential and combinatorial topology, 63-80 (1965) · Zbl 0142.41103
[21] Smale, S.: Differentiable dynamical systems. Bull. am. Math. soc. 73, 747-817 (1967) · Zbl 0202.55202
[22] Sotomayor, J.: Bifurcations of vector fields on two-dimensional manifolds. Publ. I.H.E.S. 43, 1-46 (1973) · Zbl 0279.58008
[23] Takens, F.: Singularities of vector fields. Publ. I.H.E.S. 43, 47-100 (1973) · Zbl 0279.58009