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Invariant curves for planar mappings. (English) Zbl 0891.34070

Authors’ abstract: In order to understand the dynamics of a second-order delay differential equation with a piecewise constant argument, we study the derived planar mappings and their invariant curves.

MSC:

34K10 Boundary value problems for functional-differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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[1] DOI: 10.1080/00036818808839717 · Zbl 0634.34051
[2] DOI: 10.1090/S0002-9939-1987-0877038-7
[3] Gyori I., Differential and Integral Equations 2 pp 123– (1989)
[4] Zhang F., Radovi Matematički 6 pp 347– (1990)
[5] DOI: 10.1016/0022-247X(84)90248-8 · Zbl 0557.34059
[6] Wiener J., World Scientific (1993)
[7] DOI: 10.1016/0022-247X(89)90286-2 · Zbl 0728.34077
[8] Carvalho L., Differential and Integral Equations 1 pp 359– (1988)
[9] Furumochi T., Mem. Fac. Sci. Shimane univ. 24 pp 21– (1990)
[10] Gopalsamy K., Differential and Integral Equations 4 pp 215– (1991)
[11] Gukenheimer J., Nonlinear Oscillations Dynamical Systems, and Bifurcations of Vector Fields (1983)
[12] Thompson J.M.T., Nonlinear Dynamics and Chaos, John Wiley & Sons (1986)
[13] Kuczma M., Encyclopedia of Math. & Its Applications 32 (1990)
[14] Hirsch M., Lecture Notes in Math. 583 (1977)
[15] Palis J., Geometric Theory of Dynamical Systems (1982) · Zbl 0491.58001
[16] Zhang, W. 1993.Generalized exponential dichotomies and invariant manifolds for differential equations.Vol. 22, 1–45. China advances in Math · Zbl 0791.34039
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