Topic
Regular map
About: Regular map is a research topic. Over the lifetime, 177 publications have been published within this topic receiving 4761 citations.
Papers published on a yearly basis
Papers
Book•
1 Jan 1957
TL;DR: In this article, the authors present a systematic enumeration of cosets based on the following groups: cyclic, Dicyclic and Metacyclic groups, Graphs, Maps, Cayley Diagrams, Hyperbolic Tessellations and Fundamental Groups.
Abstract: 1. Cyclic, Dicyclic and Metacyclic Groups.- 2. Systematic Enumeration of Cosets.- 3. Graphs, Maps and Cayley Diagrams.- 4. Abstract Crystallography.- 5. Hyperbolic Tessellations and Fundamental Groups.- 6. The Symmetric, Alternating, and other Special Groups.- 7. Modular and Linear Fractional Groups.- 8. Regular Maps.- 9. Groups Generated by Reflections.- Tables 1-12.
1,988 citations
365 citations
335 citations
TL;DR: In this article, it was shown that almost any real quadratic map Pc : z t-x2 + c, c c [-2,1/4], has either an attracting cycle or an absolutely continuous invariant measure.
Abstract: In this paper we complete a program to study measurable dynamics in the real quadratic family. Our goal was to prove that almost any real quadratic map Pc : z t- x2 + c, c c [-2,1/4], has either an attracting cycle or an absolutely continuous invariant measure. The final step, completed here, is to prove that the set of infinitely renormalizable parametric values c c [-2,1/4] has zero Lebesgue measure. We derive this from a Renormalization Theorem which asserts uniform hyperbolicity of the full renormalization operator. This theorem gives the most general real version of the Feigenbaum-Coullet-Tresser universality, simultanuously for all combinatorial types.
217 citations
151 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 5 |
| 2020 | 6 |
| 2019 | 3 |
| 2018 | 11 |
| 2017 | 8 |
| 2016 | 10 |