Combinatorics, geometry and attractors of quasi-quadratic maps
| dc.creator | Lyubich, Mikhail | |
| dc.date | 1992-12-06 | |
| dc.date.accessioned | 2026-07-07T09:14:51Z | |
| dc.date.available | 2026-07-07T09:14:51Z | |
| dc.description | The Milnor problem on one-dimensional attractors is solved for S-unimodal maps with a non-degenerate critical point c. It provides us with a complete understanding of the possible limit behavior for Lebesgue almost every point. This theorem follows from a geometric study of the critical set $ω(c)$ of a "non-renormalizable" map. It is proven that the scaling factors characterizing the geometry of this set go down to 0 at least exponentially. This resolves the problem of the non-linearity control in small scales. The proofs strongly involve ideas from renormalization theory and holomorphic dynamics. | |
| dc.identifier | https://arxiv.org/abs/math/9212210 | |
| dc.identifier | http://arxiv.org/abs/math/9212210 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152826 | |
| dc.subject | Dynamical Systems | |
| dc.title | Combinatorics, geometry and attractors of quasi-quadratic maps | |
| dc.type | text |