Abstract
A differential equation of the form x' = f(t, x) with the right part f(t, x) having continuous derivatives up to r-th order inclusive, 1-periodic in t, we identify with the function f and consider as an element of the Banach space Er of such functions with the Cr-norm. The equation f defines a dynamical system on a cylindrical phase space. An equation f is called rough if any equation close enough to it is topologically equivalent to f, that is, it has the same topological structure of the phase portrait. An
Publisher
FSAEIHE South Ural State University (National Research University)
Reference12 articles.
1. 1. Andronov A.A., Leontovich E.A. K teorii izmeneniya kachestvennoy struktury razbieniya ploskosti na traektorii (On the Theory of Changing the Qualitative Structure of the Division of a Plane into Trajectories). Doklady AN SSSR, 1938, Vol. 21, no. 9, pp. 427-430. (in Russ.).
2. 2. Andronov A.A., Leontovich E.A., Gordon I.I., Maier A.G. Theory of Bifurcations of Dynamic Systems on a Plane. Halsted Press [A division of John Wiley & Sons] and Israel Program for Scientific Translations, New York-Toronto, Ont. and Jerusalem-London, 1973, 482 p.
3. 3. Peixoto M. Structural Stability on Two-Dimensional Manifolds. Topology, 1962, Vol. 1, no. 2, pp. 101-120.
4. 4. Aranson S.H. The Absence of Nonclosed Poison-Stable Semitrajectories and Trajectories Doubly Asymptotic to a Double Limit Cycle for Dynamical Systems of the First Degree of Structural Instability on Orientable Two-Dimensional Manifolds. Mathematics of the USSR-Sbornik, 1968, Vol. 5, no. 2, pp. 205-219. DOI: 10.1070/SM1968v005n02ABEH002593
5. 5. Sotomayor J. Generic One-Parameter Families of Vector Fields on Two-Dimensional Manifolds. Publications Mathématiques de l'Institut des Hautes Études Scientifiques, 1974. Vol. 43, pp. 5-46. DOI: 10.1007/BF02684365