Back to Search
Start Over
Renormalization in the golden-mean semi-Siegel Hénon family: universality and non-rigidity
- Source :
- Ergodic Theory and Dynamical Systems. 40:1108-1152
- Publication Year :
- 2018
- Publisher :
- Cambridge University Press (CUP), 2018.
-
Abstract
- It was recently shown in Gaidashev and Yampolsky [Golden mean Siegel disk universality and renormalization. Preprint, 2016, arXiv:1604.00717] that appropriately defined renormalizations of a sufficiently dissipative golden-mean semi-Siegel Hénon map converge super-exponentially fast to a one-dimensional renormalization fixed point. In this paper, we show that the asymptotic two-dimensional form of these renormalizations is universal and is parameterized by the average Jacobian. This is similar to the limit behavior of period-doubling renormalizations in the Hénon family considered in de Carvalho et al [Renormalization in the Hénon family, I: universality but non-rigidity. J. Stat. Phys.121 (5/6) (2006), 611–669]. As an application of our result, we prove that the boundary of the golden-mean Siegel disk of a dissipative Hénon map is non-smoothly rigid.
- Subjects :
- Applied Mathematics
General Mathematics
010102 general mathematics
Parameterized complexity
Fixed point
01 natural sciences
Universality (dynamical systems)
Hénon map
Renormalization
symbols.namesake
0103 physical sciences
Jacobian matrix and determinant
Dissipative system
symbols
Golden ratio
010307 mathematical physics
0101 mathematics
Mathematics
Mathematical physics
Subjects
Details
- ISSN :
- 14694417 and 01433857
- Volume :
- 40
- Database :
- OpenAIRE
- Journal :
- Ergodic Theory and Dynamical Systems
- Accession number :
- edsair.doi...........0877144f303d54fd31156d6b6048dcfe