$$\rho $$ -bounded orbits and minimal sets for generalized quasiperiodically forced circle maps广义准周期强迫圆映射的有界轨道和最小集

IF 1.4 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2024-05-13 DOI:10.1007/s13324-024-00916-z

Tong Zhou, Guangxun Sun

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引用次数: 0

摘要

我们研究广义的准周期强迫圆图（f:\mathbb {T}^{m}\times \mathbb {T}^{1}\rightarrow \mathbb {T}^{m}\times \mathbb {T}^{1}\ ），它是准周期强迫圆图的自然广义化。我们的主要目的是证明对于纤维旋转集内部的每个 $\rho $，都有一个极小集，使得极小集上的每个轨道都是$\rho $有界的。

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$\rho $-bounded orbits and minimal sets for generalized quasiperiodically forced circle maps

We study the generalized quasiperiodically forced circle map $f:\mathbb {T}^{m}\times \mathbb {T}^{1}\rightarrow \mathbb {T}^{m}\times \mathbb {T}^{1}$, which is a natural generalization of the quasiperiodically forced circle map. Our main aim is to show that for each $\rho $ in the interior of the fibred rotation set, there is a minimal set such that each orbit on the minimal set is $\rho $-bounded.

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来源期刊

Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

0.00%

发文量

122

期刊介绍： Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.