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11.
Jaume Giné 《Journal of Mathematical Analysis and Applications》2006,324(1):739-745
In this note we give a family of planar polynomial differential systems with a prescribed hyperbolic limit cycle. This family constitutes a corrected and wider version of an example given in the work [M.A. Abdelkader, Relaxation oscillators with exact limit cycles, J. Math. Anal. Appl. 218 (1998) 308-312]. The result given in this note may be used to construct models of Liénard differential equations exhibiting a desired limit cycle. 相似文献
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Romain Joly Genevive Raugel 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2010,27(6):539-1440
In this paper, we show that, for scalar reaction–diffusion equations ut=uxx+f(x,u,ux) on the circle S1, the Morse–Smale property is generic with respect to the non-linearity f. In Czaja and Rocha (2008) [13], Czaja and Rocha have proved that any connecting orbit, which connects two hyperbolic periodic orbits, is transverse and that there does not exist any homoclinic orbit, connecting a hyperbolic periodic orbit to itself. In Joly and Raugel (2010) [31], we have shown that, generically with respect to the non-linearity f, all the equilibria and periodic orbits are hyperbolic. Here we complete these results by showing that any connecting orbit between two hyperbolic equilibria with distinct Morse indices or between a hyperbolic equilibrium and a hyperbolic periodic orbit is automatically transverse. We also show that, generically with respect to f, there does not exist any connection between equilibria with the same Morse index. The above properties, together with the existence of a compact global attractor and the Poincaré–Bendixson property, allow us to deduce that, generically with respect to f, the non-wandering set consists in a finite number of hyperbolic equilibria and periodic orbits. The main tools in the proofs include the lap number property, exponential dichotomies and the Sard–Smale theorem. The proofs also require a careful analysis of the asymptotic behavior of solutions of the linearized equations along the connecting orbits. 相似文献
13.
H. Giacomini 《Journal of Differential Equations》2005,213(2):368-388
We consider a planar differential system , , where P and Q are C1 functions in some open set U⊆R2, and . Let γ be a periodic orbit of the system in U. Let f(x,y):U⊆R2→R be a C1 function such that
14.
In this paper we give a classification of special endomorphisms of nil-manifolds:Let f:N/Γ → N/Γ be a covering map of a nil-manifold and denote by A:N/Γ → N/Γ the nil-endomorphism which is homotopic to f. If f is a special T A-map, then A is a hyperbolic nil-endomorphism and f is topologically conjugate to A. 相似文献
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One derives the governing equations and the Rankine–Hugoniot conditions for a mixture of two miscible fluids using an extended form of Hamilton's principle of least action. The Lagrangian is constructed as the difference between the kinetic energy and a potential depending on the relative velocity of components. To obtain the governing equations and the jump conditions one uses two reference frames related with the Lagrangian coordinates of each component. Under some hypotheses on flow properties one proves the hyperbolicity of the governing system for small relative velocity of phases. 相似文献
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《Expositiones Mathematicae》2022,40(2):254-264
Addressing a question of Zaremsky, we give conditions on a finite simplicial graph which guarantee that the associated matching arc complex is connected and hyperbolic. 相似文献
19.
Yi-Chiuan CHEN 《数学年刊B辑(英文版)》2007,28(2):219-224
The embedding of the Bernoulli shift into the logistic map x→μx(1- x) forμ> 4 is reinterpreted by the theory of anti-integrability: it is inherited from the anti-integrable limitμ→∞. 相似文献
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José M. Rodríguez José M. Sigarreta Jean-Marie Vilaire María Villeta 《Discrete Mathematics》2011,311(4):4592
If X is a geodesic metric space and x1,x2,x3∈X, a geodesic triangleT={x1,x2,x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is δ-hyperbolic (in the Gromov sense) if, for every geodesic triangle T in X, every side of T is contained in a δ-neighborhood of the union of the other two sides. We denote by δ(X) the sharpest hyperbolicity constant of X, i.e. . In this paper, we obtain several tight bounds for the hyperbolicity constant of a graph and precise values of this constant for some important families of graphs. In particular, we investigate the relationship between the hyperbolicity constant of a graph and its number of edges, diameter and cycles. As a consequence of our results, we show that if G is any graph with m edges with lengths , then , and if and only if G is isomorphic to Cm. Moreover, we prove the inequality for every graph, and we use this inequality in order to compute the precise value δ(G) for some common graphs. 相似文献