On Polynomial Double Periodic Differential Equations
Author(s):
Eugenii Konstantinovich Ershov
St. Petersburg State University of Architecture and Civil Engineering,
Russia
ershov@ee13858.spb.edu
Abstract:
In the paper we consider first order ordinary differential equations
with right-hand side that is periodic in both variables and
is a trigonometric polynom of degree n with respect to the dependent variable.
We prove that every such an equation with rational rotation number p/q,
where q does not exceed n, can be approximated by a structurally stable
polynomial equation of degree n. It is also shown that in the case
when n=1 the existence of such an approximation implies q=1.
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