Bifurcations of periodic solutions for plane mappings

In this paper,using some techniques,we prove that there exists the regular homoclinic point for Taylor mapping with 4相似文献   

一类Hamilton系统的同宿解存在性

We study the existence of homoclinic orbits for some Hamiltonian system.A homoclinic orbit is obtained as a limit of 2kT-periodic solutions of a sequence of systems of differential equations.     

THE POINCAR BIFURCATION OF A CUBIC HAMILTONIAN SYSTEM WITH HOMOCLINIC LOOP

In this paper, we discuss the Poincare bifurcation of a cubic Hamiltonian system with homoclinic loop. We prove that the system can generate at most seven limit cycles after a small perturbation of general cubic polynomials.     

Codimension 3 Nontwisted Double Homoclinic Loops Bifurcations with Resonant Eigenvalues

This paper presents the nontwisted double-homoclinic-loop bifurcations with resonant eigenvalues in four dimensional vector fields. The Poincaré map is established to solve various problems in double-homoclinic-loop bifurcations with codimension 3. Bifurcation diagrams and bifurcation curves are given. Dedicated to Professor Zhifen Zhang on the occasion of her 80th birthday     

Homoclinic orbits for a perturbed quintic-cubic nonlinear Schrödinger equation

The existence of homoclinic orbits for a perturbed cubic-quintic nonlinear Schrödinger equation with even periodic boundary conditions under the generalized parameters conditions is established. We combined geometric singular perturbation theory, Melnikov analysis, and integrable theory to prove the persistence of homoclinic orbits.     

平面自治系统同宿轨族的存在唯一性

本文研究一般平面自治系统     

Homoclinic Orbit in a Six Dimensional Model of a Perturbed Higher-order NLS Equation

In this paper, the perturbed higher-order NLS equation with periodic boundary condition is considered. The existence of the homoclinic orbits for the truncation equation is established by Melnikov analysis and geometric singular perturbation theory.     

Solitary Wave in Linear ODE with Variable Coefficients

In this paper, the linear ordinary differential equations with variable coefficients are obtained from thecontrolling equations satisfied by wavelet transform or atmospheric internal gravity waves, and these linear equationscan be further transformed into Weber equations. From Weber equations, the homoclinic orbit solutions can be derived,so the solitary wave solutions to linear equations with variable coefficients are obtained.     

On the number of limit cycles in double homoclinic bifurcations

LetL be a double homoclinic loop of a Hamiltonian system on the plane. We obtain a condition under whichL generates at most two large limit cycles by perturbations. We also give conditions for the existence of at most five or six limit cycles which appear nearL under perturbations.     

Resonant Homoclinic Flip Bifurcations

This paper studies three-parameter unfoldings of resonant orbit flip and inclination flip homoclinic orbits. First, all known results on codimension-two unfoldings of homoclinic flip bifurcations are presented. Then we show that the orbit flip and inclination flip both feature the creation and destruction of a cusp horseshoe. Furthermore, we show near which resonant flip bifurcations a homoclinic-doubling cascade occurs. This allows us to glue the respective codimension-two unfoldings of homoclinic flip bifurcations together on a sphere around the central singularity. The so obtained three-parameter unfoldings are still conjectural in part but constitute the simplest, consistent glueings.