Loading...
Please wait, while we are loading the content...
Similar Documents
On the solenoidal representation of the hyperbolic attractor of a diffeomorphism of the sphere
| Content Provider | Semantic Scholar |
|---|---|
| Author | Fedotov, A. G. |
| Copyright Year | 2017 |
| Abstract | The study of one-dimensional hyperbolic attractors of diffeomorphisms of a surface stems from the example due to Smale [1] of a DA (derived from Anosov) diffeomorphism of the torus. Williams [2], [3] gave an abstract description of expanding hyperbolic attractors by using inverse spectra of mappings of smooth ramified manifolds. These objects were dubbed Williams solenoids (generalized solenoids). An example of a one-dimensional hyperbolic attractor on the sphere was constructed by Plykin [4]. Plykin’s approach was further developed in his paper [5] and in Zhirov’s papers (see [6] and references therein). The main obstructions to one-dimensional generalized solenoids arise when they are realized in two-dimensional dynamical systems. The papers [7] and [8] establish some necessary conditions as well as sufficient conditions for the existence of such a realization. The aim of the present paper is to carry out further study of solenoidal representations of hyperbolic attractor on the sphere. Let K = V n i=1S 1 i be a bouquet of circles, and let φ : K → K be a mapping such that |
| Starting Page | 181 |
| Ending Page | 183 |
| Page Count | 3 |
| File Format | PDF HTM / HTML |
| DOI | 10.1134/S0001434617010217 |
| Alternate Webpage(s) | https://www.hse.ru/mirror/pubs/lib/data/access/ram/ticket/50/1544321049534b8c6616027c6bae157e0e53f329ee/%D0%9C%D0%B0%D1%82%20%D0%B7%D0%B0%D0%BC%D0%B5%D1%82%D0%BA%D0%B8%202%20%D0%B0%D0%BD%D0%B3%D0%BB.pdf |
| Alternate Webpage(s) | https://doi.org/10.1134/S0001434617010217 |
| Volume Number | 101 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
