共查询到20条相似文献,搜索用时 15 毫秒
1.
M. Sabatini 《Proceedings of the American Mathematical Society》2006,134(2):531-539
A necessary and sufficient condition for the period function's monotonicity on a period annulus is given. The approach is based on the theory of normalizers, but is applicable without actually knowing a normalizer. Some applications to polynomial and Hamiltonian systems are presented.
2.
Maoan Han 《Journal of Mathematical Analysis and Applications》2010,368(2):491-497
We describe a method based on algorithms of computational algebra for obtaining an upper bound for the number of limit cycles bifurcating from a center or a focus of polynomial vector field. We apply it to a cubic system depending on six parameters and prove that in the generic case at most six limit cycles can bifurcate from any center or focus at the origin of the system. 相似文献
3.
In this paper,we consider Li′enard systems of the form dx/dt=y,dy/dt=x+bx3-x5+ε(α+βx2+γx4)y,where b∈R,0|ε|1,(α,β,γ)∈D∈R3 and D is bounded.We prove that for |b|1(b0) the least upper bound of the number of isolated zeros of the related Abelian integrals I(h)=∮Γh(α+βx2+γx4)ydx is 2(counting the multiplicity) and this upper bound is a sharp one. 相似文献
4.
Alina Carmen Cojocaru 《Transactions of the American Mathematical Society》2003,355(7):2651-2662
Let be an elliptic curve defined over and with complex multiplication. For a prime of good reduction, let be the reduction of modulo We find the density of the primes for which is a cyclic group. An asymptotic formula for these primes had been obtained conditionally by J.-P. Serre in 1976, and unconditionally by Ram Murty in 1979. The aim of this paper is to give a new simpler unconditional proof of this asymptotic formula and also to provide explicit error terms in the formula.
5.
Viktor Levandovskyy 《Journal of Differential Equations》2009,246(3):1274-1287
We present a method for investigating the cyclicity of an elementary focus or center of a polynomial system of differential equations by means of complexification of the system and application of algorithms of computational algebra, showing an approach to treating the case that the Bautin ideal B of focus quantities is not a radical ideal (more precisely, when the ideal BK is not radical, where BK is the ideal generated by the shortest initial string of focus quantities that, like the Bautin ideal, determines the center variety). We illustrate the method with a family of cubic systems. 相似文献
6.
Jaume Llibre 《Journal of Mathematical Analysis and Applications》2009,357(2):427-189
In this paper we classify the centers, the cyclicity of their Hopf bifurcation and the isochronicity of the polynomial differential systems in R2 of degree d that in complex notation z=x+iy can be written as
7.
Linping PENG 《Frontiers of Mathematics in China》2011,6(5):911-930
In this paper, we study a reversible and non-Hamitonian system with a period annulus bounded by a hemicycle in the Poincaré disk. It is proved that the cyclicity of the period annulus under quadratic perturbations is equal to two. This verifies some results of the conjecture given by Gautier et al. 相似文献
8.
Anna Cima Armengol Gasull Víctor Mañosa 《Journal of Mathematical Analysis and Applications》2018,457(1):568-584
We introduce the concept of 2-cyclicity for families of one-dimensional maps with a non-hyperbolic fixed point by analogy to the cyclicity for families of planar vector fields with a weak focus. This new concept is useful in order to study the number of 2-periodic orbits that can bifurcate from the fixed point. As an application we study the 2-cyclicity of some natural families of polynomial maps. 相似文献
9.
Li Qin ZHAO 《数学学报(英文版)》2005,21(3):507-516
This paper deals with the cyclicity of a kind of degenerate planar polycycles through a saddle-node and two hyperbolic saddles, where the hyperbolicity ratio of the saddle (which connects the saddle-node with hp-connection) is equal to 1 and that of the other saddle is irrational. It is obtained that the cyclicity of this kind of polycycle is no more than 5 if the hp-connection keeps unbroken under the C^∞ perturbations. 相似文献
10.
Xabier Garaizar 《Applicable analysis》2013,92(4):211-240
We study questions of degeneracy and bifurcation for radial solutions of the semilinear elliptic equation ?u(x) + f(u(x)) = 0, x isin; [math001], [math001]an annulus in Rn, with homogeneous Dirichlet boundary conditions. For certain nonlinearities f(u), we prove existence of degenerate radial solutions u (for which the kernel of the linearized operator Lz = ?z + [math001](u)z, z isin; C2We study questions of degeneracy and bifurcation for radial solutions of the semilinear elliptic equation ?u(x) + f(u(x)) = 0, x isin; [math001], [math001]an annulus in Rn, with homogeneous Dirichlet boundary conditions. For certain nonlinearities f(u), we prove existence of degenerate radial solutions u (for which the kernel of the linearized operator Lz = ?z + [math001](u)z, z isin; C2$0([math001]), is non-trivial) and existence of nonradial solutions for the semi-linear equation. These nonradial (asymmetric) solutions are obtained via a bifurcation procedure from the radial (symmetric) ones. This phenomena is called symmetry-breaking. The bifurcation results are proved by a Conley index argument 相似文献
11.
Al3-manifOldsandsurfacesconsideredinthisPaperareassumedtobecompactandori-entable,andallconcePtsandnotationsnotdefinedinthepaperareStandardfsee,forexample[2,3j.AcompressionbodyHisconstructedbyadding2-handlestoSXIalongacollectionofpairwisdisjointsimpleclosedcurvesonSX{o},andcaPpingoffanyresulting2-spherebound-arycomponentSwith3-balls,whereSisaconnectedclosedorientablesurface.ThecomponentSX{1}Of8Hisdenoted8 Handthesurface8H-8 H,whichmayormaynotbeconnect-ed,isdenoted8H.If8H=gi,Hisahandleb… 相似文献
12.
Probabilistic temporal networks: A unified framework for reasoning with time and uncertainty 总被引:6,自引:0,他引:6
Complex real-world systems consist of collections of interacting processes/events. These processes change over time in response to both internal and external stimuli as well as to the passage of time itself. Many domains such as real-time systems diagnosis, story understanding, and financial forecasting require the capability to model complex systems under a unified framework to deal with both time and uncertainty. Current models for uncertainty and current models for time already provide rich languages to capture uncertainty and temporal information, respectively. Unfortunately, these semantics have made it extremely difficult to unify time and uncertainty in a way which cleanly and adequately models the problem domains at hand. Existing approaches suffer from significant trade offs between strong semantics for uncertainty and strong semantics for time. In this paper, we explore a new model, the Probabilistic Temporal Network (PTN), for representing temporal and atemporal information while fully embracing probabilistic semantics. The model allows representation of time constrained causality, of when and if events occur, and of the periodic and recurrent nature of processes. 相似文献
13.
The radiative transfer equation in a two-dimensional rectangular annulus medium is solved numerically. The numerical method is based on a finite difference scheme and a product quadrature discrete-ordinate scheme. The discretized equation of transfer is solved iteratively to give the radiation intensity. The medium is assumed to absorb, emit, and anisotropically scatter radiation. It is exposed to diffusely emitting and diffusely reflecting boundaries. The results of the total intensity for various radiative parameters are presented. The method can be modified easily to solve the rectangular medium without the annulus. Our results in this case compare very well with those of Crosbie et al. [1], Thynell et al. [2], and Wu [3]. 相似文献
14.
The annulus and disk complex is defined and researched. Especially, we prove that this complex is contractible and quasi-convex in the curve complex. 相似文献
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16.
Werestrictourconsiderationtoorientableandcompactcategory .Fordefinitionsandterminology ,seeforexample ,[1 ]and [2 ]. LetSbeaclosedorientablesurfacewithpositivegenus .Inthispaper ,MalwaysdenotesS×I ,andS0 =S× 0 ,S1=S× 1 .AnannulusAinMwithitstwoboundarieslyinginS0andS1r… 相似文献
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18.
本文应用摄动方法研究了非牛顿流体在偏心环形空间中轴向层流的流动规律.文中以相对偏心度ε作为摄动参数,得到了其流场、极值速度、压力梯度等流动参数的一阶解. 相似文献
19.
LUND Mark 《中国科学 数学(英文版)》2010,(3)
In this survey paper, we discuss the recent development of Nevanlinna theory of meromorphic functions on annuli, which extends results in Nevanlinna theory in the complex plane or in a disk. In particular, we show that the approach taken on annuli is a unified treatment of functions meromorphic in the complex plane, a disk and an annulus. It allows one to obtain many results in the complex plane and in a disk as corollaries of our results in annuli. 相似文献
20.
In this paper we consider analytic vector fields X0 having a non-degenerate center point e. We estimate the maximum number of small amplitude limit cycles, i.e., limit cycles that arise after small perturbations of X0 from e. When the perturbation (Xλ) is fixed, this number is referred to as the cyclicity of Xλ at e for λ near 0. In this paper, we study the so-called absolute cyclicity; i.e., an upper bound for the cyclicity of any perturbation Xλ for which the set defined by the center conditions is a fixed linear variety. It is known that the zero-set of the Lyapunov quantities correspond to the center conditions (Caubergh and Dumortier (2004) [6]). If the ideal generated by the Lyapunov quantities is regular, then the absolute cyclicity is the dimension of this so-called Lyapunov ideal minus 1. Here we study the absolute cyclicity in case that the Lyapunov ideal is not regular. 相似文献