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Bifurcations from an invariant circle for two-parameter families of maps of the plane: a computer-assisted study. (English) Zbl 0499.70034

MSC:
70K50Transition to stochasticity (general mechanics)
37C70Attractors and repellers, topological structure
37D45Strange attractors, chaotic dynamics
54C05Continuous maps
54C25Embeddings of topological spaces
58C25Differentiable maps on manifolds (global analysis)
References:
[1]Arnol’d, V.I.: Loss of stability of self-oscillations close to resonance and versal deformations of equivarient vector fields. Funct. Anal. Appl.11, 1-10 (1977) · Zbl 0411.58013 · doi:10.1007/BF01081886
[2]Aronson, D.G., Chory, M.A., Hall, G.R., McGehee, R.P.: A discrete dynamical system with subtly wild behavior. New approaches to nonlinear problems in dynamics, Holmes, P. (ed.). SIAM 1980
[3]Bowen, R.: On axiomA diffeomorphisms. CBMS Regional Conference Series in Mathematics, No. 35. Providence, Rhode Island: Am. Math. Soc. 1978
[4]Conley, C.: Isolated invariant sets and the Morse index. CBMS Regional Conference Series in Mathematics, No. 38. Providence, Rhode Island: Am. Math. Soc. 1978
[5]Conley, C.: Hyperbolic sets and shift automorphisms. Dynamical systems: theory and applications. In: Lecture Notes in Physics, Vol. 38, Moser, J. (ed.), pp. 539-549. Berlin, Heidelberg, New York: Springer 1975
[6]Curry, J., Yorke, J.: A transition from Hopf bifurcation to chaos: computer experiments on maps inR 2. The structure of attractors in dynamical systems. In: Lecture Notes in Mathematics, Vol. 668, pp. 48-68. Berlin, Heidelberg, New York: Springer 1978
[7]Fenichel, N.: Persistence and smoothness of invariant manifolds for flows, Ind. Univ. Math. J.21, 193-226 (1971) · Zbl 0246.58015 · doi:10.1512/iumj.1971.21.21017
[8]Flaherty, J., Hoppensteadt, F.: Frequency entrainment of a forced van der Pol oscillator. Stud. Appl. Math.58, 5-15 (1978)
[9]Guckenheimer, J.: A strange, strange attractor. The Hopf bifurcation theorem and its applications, Marsden, J., McCracken, M. (eds.), pp. 368-381. Berlin, Heidelberg, New York: Springer 1976
[10]Guckenheimer, J.: On the bifurcation of maps of the interval. Invent. Math.39, 165-178 (1977) · Zbl 0354.58013 · doi:10.1007/BF01390107
[11]Guckenheimer, J., Williams, R.F.: Structural stability of Lorenz attractors. Publ. Math. I.H.E.S.50, 307-320 (1979)
[12]Hartman, P.: Ordinary differential equations. New York: Wiley 1964
[13]Hénon, M.: A two-dimensional mapping with a strange attractor. Commun. Math. Phys.50, 67-77 (1976)
[14]Iooss, G.: Topics in bifurcation of maps and applications. Math. Stud. 36. Amsterdam: North-Holland 1979
[15]Levi, M.: Qualitative analysis of the periodically forced relaxation oscillators. Mem. AMS244, 1981
[16]Levinson, N.: A second order differential equation with singular solutions. Ann. Math.50, 127-153 (1949) · Zbl 0045.36501 · doi:10.2307/1969357
[17]Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci.20, 130-141 (1963) · doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
[18]Maynard Smith, J.: Mathematical ideas in biology. Cambridge: Cambridge University Press 1971
[19]Milnor, J., Thurston, W.: On iterated maps of the interval, I, II (preprint)
[20]Newhouse, S.: Diffeomorphisms with infinitely many sinks. Topology13, 9-18 (1974) · Zbl 0275.58016 · doi:10.1016/0040-9383(74)90034-2
[21]Poincaré, H.: Les méthodes nouvelles de la mécanique céleste. Vol. 3. Paris: Gauthiers-Villars 1899
[22]Pounder, J.R., Rogers, T.D.: The geometry of chaos: dynamics of a nonlinear second-order difference equation. Bull. Math. Biol.42, 551-597 (1980)
[23]Rademacher, H.: Lectures on elementary number theory. New York: Blaisdell 1964
[24]Ruelle, D.: A measure associated with axiomA attractors. Am. J. Math.98, 19-64 (1976) · Zbl 0355.58010 · doi:10.2307/2373810
[25]Ruelle, D.: Strange attractors. The Mathematical Intelligencer2, 126-137 (1980) · Zbl 0487.58014 · doi:10.1007/BF03023053
[26]Ruelle, D., Takens, F.: On the nature of turbulence. Commun. Math. Phys.20, 167-192 (1971) · Zbl 0223.76041 · doi:10.1007/BF01646553
[27]Smale, S.: Diffeomorphisms with many periodic points. Differential and combinatorial topology, pp. 63-80. Princeton, N.J.: Princeton University Press 1965
[28]Stein, P.R., Ulam, S.M.: Nonlinear transformation studies on electronic computers. Rozprawy Matem.39, 3-65 (1964)
[29]Takens, F.: Forced oscillations and bifurcations. Applications of global analysis. Commun. Math. Inst. Rikjsuniversitat Utrecht
[30]Williams, R.F.: Expanding attractors. Publ. Math. I.H.E.S.43, 169-203 (1974); see also Proceedings of the Mount Aigual Conference on Differential Topology, Univ. of Montepellier, 1969
[31]Zharkovsky, A.N.: Coexistence of cycles of a continuous map of a line into itself. Ukrain. Mat. Z.16, 61-71 (1974)