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Every Period Annulus is Both Reversible and Symmetric [PDF]
Qualitative Theory of Dynamical Systems, 2015 We prove that for every planar differential system with a period annulus there exists an involution $σ$ such that the system is $σ$-symmetric. We also prove that for for every planar differential system with a period annulus there exist infinitely many involutions $σ$ such that the system is $σ$-reversible.
Marco Sabatini
exaly +4 more sources
The Cyclicity of the Period Annulus of the Quadratic Hamiltonian Triangle
Journal of Differential Equations, 1996 The paper investigates the number of limit cycles for small quadratic perturbations of quadratic Hamiltonian systems \(x' = H_y + \varepsilon f(x,y,\varepsilon)\), \(y' = -H_x + \varepsilon g(x,y,\varepsilon)\), where \(H\) has the form \(H = l_1 l_2 l_3\) with \(l_j = a_j + b_j + c_j\). This case is known as the Hamiltonian triangle.
Iliya D Iliev
exaly +2 more sources
Perturbation of a Period Annulus with a Unique Two-Saddle Cycle in Higher Order Hamiltonian
Complexity, 2019 In this paper, we study the number of limit cycles emerging from the period annulus by perturbing the Hamiltonian system x˙=y,y˙=x(x2-1)(x2+1)(x2+2). The period annulus has a heteroclinic cycle connecting two hyperbolic saddles as the outer boundary.
Hongying Zhu +3 more
doaj +2 more sources