MathSciDoc: An Archive for Mathematician ∫

 
Log In
Sign Up
Help
Go
 

Whitney's critical set in fractal

Yong Lin Information School, Renmin University of China, Beijing 100872, PR China Xi Lifeng Institute of Mathematics, Zhejiang Wanli University, Ningbo 315101, PR China

TBD mathscidoc:2207.43004

Chaos, Solitons & Fractals, 14, (7), 995-1006, 2002.10
The problem is concerned about how large (e.g. the Hausdorff dimension) is Whitney's critical set contained in a given fractal. For this, we prove that the Moran arc, an arc containing a Moran set, is a Whitney's critical set. The excellent open set condition is defined, when the condition holds, the associated self-similar set contains a Whitney's critical subset of full dimension. As its application, the Sierpinski gasket and Koch curve have Whitney's critical subset of full dimension. Finally, we provide a self-similar tree which never contains any Whitney's critical set.
No keywords uploaded!
[ Download ] [ 2022-07-07 11:04:04 uploaded by yonglin ] [ 247 downloads ] [ 0 comments ] 
@inproceedings{yong2002whitney's,
  title={Whitney's critical set in fractal},
  author={Yong Lin, and Xi Lifeng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707110404944580548},
  booktitle={Chaos, Solitons & Fractals},
  volume={14},
  number={7},
  pages={995-1006},
  year={2002},
}
Yong Lin, and Xi Lifeng. Whitney's critical set in fractal. 2002. Vol. 14. In Chaos, Solitons & Fractals. pp.995-1006. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707110404944580548.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved