논문KCI 등재
A persistently singular map of $\mathbb{T}^n$ that is $C^2$ robustly transitive but is not $C^1$ robustly transitive
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키워드
주제분류수학
초록
Consider the high dimensional torus $\mathbb{T}^n$ and the set $\mathcal{E}$ of its endomorphisms. We construct a map in $\mathcal{E}$ that is robustly transitive if $\mathcal{E}$ is endowed with the $C^2$ topology but is not robustly transitive if $\mathcal{E}$ is endowed with the $C^1$ topology.
Abstract
Consider the high dimensional torus $\mathbb{T}^n$ and the set $\mathcal{E}$ of its endomorphisms. We construct a map in $\mathcal{E}$ that is robustly transitive if $\mathcal{E}$ is endowed with the $C^2$ topology but is not robustly transitive if $\mathcal{E}$ is endowed with the $C^1$ topology.
참고문헌 (12)
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- J. Iglesias, "Robust transitivity for endomorphisms admitting critical points", Proc. Amer. Math. Soc, (3), pp.1235~1250 (2016)[DOI]
- Jorge Iglesias, "An example of a map which is C2-robustly transitive but not C1-robustly transitive", Colloquium Mathematicum, 152(2), pp.285~297 (2018), Institute of Mathematics, Polish Academy of Sciences[DOI]
- CRISTINA LIZANA, "Robust transitivity for endomorphisms", Ergodic Theory and Dynamical Systems, 33(4), pp.1082~1114 (2013), Cambridge University Press (CUP)[DOI]
- C. Lizana, "Topological obstructions for robustly transitive endomor-phisms on surfaces", arXiv:1711.02218, ~ (2017)
- C. Lizana, "New classes of C1 robustly transitive maps with persistent critical points", arXiv:1902.06781, ~ (2019)
- Ricardo Mane, "An Ergodic Closing Lemma", The Annals of Mathematics, 116(3), pp.503~ (1982), JSTOR[DOI]
- R. Thom, "Les singularites des applications differentiables, (French)", Ann. Inst. Fourier (Grenoble), 6, pp.43~87 (1955)
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