Abstract
© 2015, Journal of Applied Analysis and Computation. All Rights Reserved. The notion of Hilbert number from polynomial differential systems in the plane of degree n can be extended to the differential equations of the form (formula presented) defined in the region of the cylinder (θ; r) ∈ θS<sup>1</sup>× ℝ where the denominator of (*) does not vanish. Here a; a<inf>0</inf>; a<inf>1</inf>;...; a<inf>n</inf> are analytic 2π–periodic functions, and the Hilbert number ℍ (n) is the supremum of the number of limit cycles that any differential equation (*) on the cylinder of degree n in the variable r can have. We prove that ℍ (n) = ∞ for all n ≥ 1.
Original language | English |
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Pages (from-to) | 141-145 |
Journal | Journal of Applied Analysis and Computation |
Volume | 5 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 2015 |
Keywords
- Averaging theory
- Hilbert number
- Periodic orbit
- Trigonometric polynomial