Multidimensional singular λ-lemma
| dc.contributor.author | Rayskin, Victoria | |
| dc.date.accessioned | 2020-10-19T16:25:14Z | |
| dc.date.available | 2020-10-19T16:25:14Z | |
| dc.date.issued | 2003-04-11 | |
| dc.description.abstract | The well-known λ-Lemma [3] states the following: Let ƒ be a C1-diffeomorphism of ℝn with a hyperbolic fixed point at 0 and m- and p-dimensional stable and unstable manifolds Ws and Wu, respectively (m + p = n). Let D be a p-disk in Wu and w be another p-disk in Wu meeting Ws at some point A transversely. Then ⋃n≥0 ƒn(w) contains p-disks arbitrarily C1-close to D. In this paper we will show that the same assertion still holds outside of an arbitrarily small neighborhood of 0, even in the case of non-transverse homoclinic intersections with finite order of contact, if we assume that 0 is a low order non-resonant point. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 9 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Rayskin, V. (2003). Multidimensional singular λ-lemma. <i>Electronic Journal of Differential Equations, 2003</i>(38), pp. 1-9. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/12799 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Homoclinic tangency | |
| dc.subject | Invariant manifolds | |
| dc.subject | Lambda-Lemma | |
| dc.subject | Order of contact | |
| dc.subject | Resonance | |
| dc.title | Multidimensional singular λ-lemma | |
| dc.type | Article |