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Medveď, Milan

On two-parametric systems of matrices and diffeomorphisms. (English) Zbl 0528.58030

Czech. Math. J. 33(108), 176-192 (1983).
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MSC:

37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
57R50 Differential topological aspects of diffeomorphisms

Keywords:

Kupka-Smale theorem; Whitney topology; eigenvalues on the unit circle; topological structure of trajectories; residual subsets

Citations:

Zbl 0202.231; Zbl 0239.58010
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Full Text: DOI EuDML

References:

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[3] В. И. Арноль\?: Лекции о бифуркациях и версальных семействах. YMH 27:5 (1972), 119 до 184. · Zbl 1170.01322
[4] В. И. Арноль\?: Потеря устойчивости автоколебаний вблизи резонанса и версальные деформации эквивариантных векторных полей. Функц. анализ и приложения, 11 : 2 (1977), 1-10. · Zbl 1170.01341
[5] Р. И. Богданов: Верцальная деформация особой точки векторного поля на плоскости в случае нулевых собственных чисел. Труды семинара им. И. Г. Петровсого, 2 (1976), 37-65. · Zbl 1170.01332
[6] Р. И. Богданов: Бифуркации предельного цикла одного семейства векторных полей на плоскости. Труды семинара им. Петровского 2 (1976), 23-35. · Zbl 1170.01332
[7] P. Brunovský: On one-parameter families of diffeomorphisms. Comm. Math. Univ. Carolinae 11 (1970), 559-582. · Zbl 0202.23104
[8] P. Brunovský: On one-parameter families of diffeomorphisms. Comm. Math. Univ. Carolinae 12 (1971), 765-784.
[9] M. Golubitsky V. Guillemin: Stable mappings and their singularities. New York 1973. · Zbl 0294.58004
[10] M. Medved: Generic properties of parametrized vector fields I. Czechoslovak Math. J., 25 (1975), 376-388.
[11] M. Medved: Generic properties of parametrized vector fields II. Czechoslovak Math. J. 26 (1976), 71-83.
[12] Z. Nitecki: Differential Dynamics-An Introduction to the Orbit Structure of Diffeomorphisms. Russian translation, Mir, Moscow 1975. · Zbl 0311.58001
[13] R. J. Sacker: On invariant surfaces and bifurcations of periodic solutions of ordinary differential equations. New York University, Report IMMNYU 333 (1964).
[14] J. Sotomayor: Generic bifurcations of dynamical systems. Dynamical Systems. Proc. Symp. Univ. Bahia, Salvador 1973, 561-582. · Zbl 0296.58007
[15] H. Whitney: Elementary structure of real algebraic varieties. Annals of Mathematics 66 (1957), 545-556. · Zbl 0078.13403 · doi:10.2307/1969908
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