Page 1

Displaying 1 – 11 of 11

Showing per page

Maximum number of limit cycles for generalized Liénard polynomial differential systems

Aziza Berbache, Ahmed Bendjeddou, Sabah Benadouane (2021)

Mathematica Bohemica

We consider limit cycles of a class of polynomial differential systems of the form x ˙ = y , y ˙ = - x - ε ( g 21 ( x ) y 2 α + 1 + f 21 ( x ) y 2 β ) - ε 2 ( g 22 ( x ) y 2 α + 1 + f 22 ( x ) y 2 β ) , where β and α are positive integers, g 2 j and f 2 j have degree m and n , respectively, for each j = 1 , 2 , and ε is a small parameter. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of the linear center x ˙ = y , y ˙ = - x using the averaging theory of first and second order.

Misiurewicz maps unfold generically (even if they are critically non-finite)

Sebastian van Strien (2000)

Fundamenta Mathematicae

We show that in normalized families of polynomial or rational maps, Misiurewicz maps (critically finite or infinite) unfold generically. For example, if f λ 0 is critically finite with non-degenerate critical point c 1 ( λ 0 ) , . . . , c n ( λ 0 ) such that f λ 0 k i ( c i ( λ 0 ) ) = p i ( λ 0 ) are hyperbolic periodic points for i = 1,...,n, then  IV-1. Age impartible......................................................................................................................................................................... 31   λ ( f λ k 1 ( c 1 ( λ ) ) - p 1 ( λ ) , . . . , f λ k d - 2 ( c d - 2 ( λ ) ) - p d - 2 ( λ ) ) is a local diffeomorphism...

Monotonicity of the period function for some planar differential systems. Part I: Conservative and quadratic systems

A. Raouf Chouikha (2005)

Applicationes Mathematicae

We first examine conditions implying monotonicity of the period function for potential systems with a center at 0 (in the whole period annulus). We also present a short comparative survey of the different criteria. We apply these results to quadratic Loud systems ( L D , F ) for various values of the parameters D and F. In the case of noncritical periods we propose an algorithm to test the monotonicity of the period function for ( L D , F ) . Our results may be viewed as a contribution to proving (or disproving) a conjecture...

Monotonicity of the period function for some planar differential systems. Part II: Liénard and related systems

A. Raouf Chouikha (2005)

Applicationes Mathematicae

We are interested in conditions under which the two-dimensional autonomous system ẋ = y, ẏ = -g(x) - f(x)y, has a local center with monotonic period function. When f and g are (non-odd) analytic functions, Christopher and Devlin [C-D] gave a simple necessary and sufficient condition for the period to be constant. We propose a simple proof of their result. Moreover, in the case when f and g are of class C³, the Liénard systems can have a monotonic period function...

Currently displaying 1 – 11 of 11

Page 1