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Nongeneric bifurcations near heterodimensional cycles with inclination flip in r 4.
| Content Provider | CiteSeerX |
|---|---|
| Author | Liu, Dan Ruan, Shigui Zhu, Deming |
| Abstract | Abstract. Nongeneric bifurcation analysis near rough heterodimensional cycles associated to two saddles in R4 is presented under inclination flip. By setting up local moving frame systems in some tubular neighborhood of unperturbed heterodimensional cycles, we construct a Poincaré return map under the nongeneric conditions and further obtain the bifurcation equations. Coexistence of a heterodimensional cycle and a unique periodic orbit is proved after perturbations. New features produced by the inclination flip that heterodimensional cycles and homoclinic orbits coexist on the same bifurcation surface are shown. It is also conjectured that homoclinic orbits associated to different equilibria coexist. 1. Introduction. Newhouse and Palis [11] were the first to consider heterodimensional cycles in dynamical systems. A heteroclinic cycle is said to be equidimensional if all saddle-type periodic points in the cycle have the same dimension of the stable manifold or unstable manifold. Otherwise, such a cycle is called heterodimensional (DÃaz [5]). Since different saddles in Rn are not necessarily identical with the dimension |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Heterodimensional Cycle Homoclinic Orbit Inclination Flip Unperturbed Heterodimensional Cycle Saddle-type Periodic Point Different Equilibrium Coexist Stable Manifold Unique Periodic Orbit Dynamical System Poincar Return Map Tubular Neighborhood Rough Heterodimensional Cycle Unstable Manifold Nongeneric Bifurcation Analysis Local Moving Frame System Bifurcation Equation Different Saddle Bifurcation Surface Nongeneric Condition Heteroclinic Cycle New Feature |
| Content Type | Text |
| Resource Type | Article |
