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We deal here with planar analytic systems which are small perturbations of a period annulus. For each transversal section Σ to the unperturbed orbits we denote by the time needed by a perturbed orbit that starts from to return to Σ. We call this the flight return time function. We say that the closed orbit Γ of is a continuable critical orbit in a family of the form if, for any and any Σ that passes through q, there exists a critical point of such that as . In this work we study this new problem of continuability.In particular we prove that a simple critical periodic orbit of is a continuable critical orbit in any family of the form . We also give sufficient conditions for the existence of a continuable critical orbit of an isochronous center . 相似文献
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Yinshan Chang Yiming Long Jian Wang 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(1):75-102
We consider a continuously differentiable curve in the space of real symplectic matrices, which is the solution of the following ODE: where and is a continuous path in the space of real matrices which are symmetric. Under a certain convexity assumption (which includes the particular case that is strictly positive definite for all ), we investigate the dynamics of the eigenvalues of when t varies, which are closely related to the stability of such Hamiltonian dynamical systems. We rigorously prove the qualitative behavior of the branching of eigenvalues and explicitly give the first order asymptotics of the eigenvalues. This generalizes classical Krein–Lyubarskii theorem on the analytic bifurcation of the Floquet multipliers under a linear perturbation of the Hamiltonian. As a corollary, we give a rigorous proof of the following statement of Ekeland: is a discrete set. 相似文献
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A revised Yau's Curvature Difference Flow is considered to deform one convex curve to another one . It is proved that this flow exists globally on time interval and the evolving curve, preserving its convexity and bounded area A, converges to a fixed limiting curve (congruent to ) as time tends to infinity, where is the area bounded by the target curve . 相似文献
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《Discrete Mathematics》2022,345(7):112893
In this paper, we study the Reconstruction Conjecture for finite simple graphs. Let Γ and be finite simple graphs with at least three vertices such that there exists a bijective map and for any , there exists an isomorphism . Then we define the associated directed graph with two kinds of arrows from the graphs Γ and , the bijective map f and the isomorphisms . By investigating the associated directed graph , we study when are the two graphs Γ and isomorphic. 相似文献
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《Discrete Mathematics》2022,345(9):112949
In this paper, we describe a result on self-conjugate -core partitions with the fixed number of corners. We also define shifted corners of a distinct partition and find formulas for the number of -core partitions and the number of -core shifted Young diagrams with the fixed number of shifted corners. 相似文献
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In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation with the critical situation that on g and p, where , is periodic and is bounded. 相似文献