Geodesic
On the structural stability relative to the space of linear differential equations with periodic coefficients
Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 20 (2017) no. 5, pp. 27-31

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Let $\textrm{LE}^n_\omega$ be the Banach space of linear non-homogeneous differential equations of order $n$ with $\omega$-periodic coefficients. We prove the following statements. The equation $l\in \textrm{LE}^n_\omega$ is structurally stable in the phase space $\Phi^2:=\mathbf{R}^n\times\mathbf{R}/\omega \mathbf{Z}(n\geq2)$ if and only if its multiplicators do not belong to the unit circle. The set of all structurally stable equations is everywhere dense in $\textrm{LE}^n_\omega$. The equation $l\in \textrm{LE}^n_\omega$ is structurally stable in the phase space $\bar{\Phi}^2:=\mathbf{RP}^2\times\mathbf{R}/\omega \mathbf{Z}$ if and only if its multiplicators are real, different and distinct from $\pm 1$. We describe also the topological equivalence classis of structurally stable in $\bar{\Phi}^2$ equations.
Keywords: linear differential equations, periodic coefficients, projective plane, structurally stable equations, multiplicators. 
V. Sh. Roitenberg. On the structural stability relative to the space of linear differential equations with periodic coefficients. Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 20 (2017) no. 5, pp. 27-31. http://geodesic.mathdoc.fr/item/VVGUM_2017_20_5_a2/
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[1] J. Palis, W. Melo, Geometric Theory of Dynamical Systems. An Introduction, Mir Publ., Moscow, 1986, 301 pp. (in Russian) | MR

[2] V. Sh. Roitenberg, “On Bifurcations of Periodic Orbits of Linear Non-Homogeneous Differential Systems With Periodic Coefficients”, Inter-university Collection of Scientific Works, Mathematics and Natural Sciences. The Theory and Practice, 11, YaSTU Publ., Yaroslavl, 2016, 66–71

[3] V. Sh. Roitenberg, “On the Structure of Space of Systems of Linear Differential Equations With Periodic Coefficients”, Science Journal of Volgograd State University. Mathematics. Physics, 1:38 (2017), 13–21 | DOI | MR