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Stable intersection of middle-α Cantor sets

Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

Abstract

We introduce a pair of middle Cantor sets which have stable intersection, while the product of their thickness is smaller than one.

Keywords:

AMSC: 37C45, 28A80, 37G25

B. Honary, C. G. Moreira and M. Pourbarat, Bull. Braz. Math. Soc. 36(3), 363 (2005). Crossref, Web of Science, Google Scholar
P. Mendes and F. Oliveira, Nonlinearity 7(2), 329 (1994). Crossref, Web of Science, Google Scholar
C. G. Moreira, Ann. Inst. H. Poincaré Anal. Non Linéaire 13(6), 741 (1996). Crossref, Web of Science, Google Scholar
C. G. Moreira, Period. Math. Hungar. 37(3), 55 (1998). Crossref, Google Scholar
C. G. Moreira and J.-C. Yoccoz, Ann. of Math. 154(1), 45 (2001). Crossref, Web of Science, Google Scholar
S. Newhouse, Non-density of axiom A(a) on S2, Global Analysis, Proceedings of Symposia in Pure Mathematics14 (American Mathematical Society, Providence, RI, 1970) pp. 191–202. Google Scholar
J. Palis , Astérisque 261 , 335 ( 2000 ) . Google Scholar
J. Palis , Ann. Inst. H. Poincaré Anal. Non Linéaire 22 , 485 ( 2005 ) . Crossref, Web of Science, Google Scholar
J. Palis and F. Takens , Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations ( Cambridge University Press , Cambridge , 1993 ) . Google Scholar
M. Pourbarat, On the arithmetic difference of middle Cantor sets , arXiv: 1306.5879v1 . Google Scholar
A. Sannami, Hokkaido Math. J. 21(1), 7 (1992). Crossref, Google Scholar
S. Zakeri, On arithmetical difference of two Cantor sets, IPM Technical Report, 1992/1 . Google Scholar