Voir la notice de l'article provenant de la source Czech Digital Mathematics Library
MR ZblKeywords: Li-Yorke chaos; Hausdorff dimension
Neunhäuserer, J. Li-Yorke pairs of full Hausdorff dimension for some chaotic dynamical systems. Mathematica Bohemica, Tome 135 (2010) no. 3, pp. 279-289. doi: 10.21136/MB.2010.140704
@article{10_21136_MB_2010_140704,
author = {Neunh\"auserer, J.},
title = {Li-Yorke pairs of full {Hausdorff} dimension for some chaotic dynamical systems},
journal = {Mathematica Bohemica},
pages = {279--289},
year = {2010},
volume = {135},
number = {3},
doi = {10.21136/MB.2010.140704},
mrnumber = {2683639},
zbl = {1224.37011},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2010.140704/}
}
TY - JOUR AU - Neunhäuserer, J. TI - Li-Yorke pairs of full Hausdorff dimension for some chaotic dynamical systems JO - Mathematica Bohemica PY - 2010 SP - 279 EP - 289 VL - 135 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.21136/MB.2010.140704/ DO - 10.21136/MB.2010.140704 LA - en ID - 10_21136_MB_2010_140704 ER -
[1] Blanchard, F., Glasner, E., Kolyada, S., Maass, A.: On Li-Yorke pairs. J. Reine Angew. Math. 547 51-68 (2002). | MR | Zbl
[2] Blanchard, F., Huang, W., Snoah, L.: Topological size of scrambled sets. Colloquium Mathematicum 110 293-361 (2008). | DOI | MR
[3] Falconer, K.: Fractal Geometry: Mathematical Foundations and Applications. Wiley, New York (1990). | MR | Zbl
[4] Hutchinson, J. E.: Fractals and self-similarity. Indiana Univ. Math. J. 30 271-280 (1981). | DOI | MR | Zbl
[5] Katok, A., Hasselblatt, B.: Introduction to Modern Theory of Dynamical Systems. Cambridge University Press (1995). | MR
[6] Li, T.-Y., Yorke, J. A.: Period three implies chaos. Amer. Math. Monthly 82 985-992 (1975). | DOI | MR | Zbl
[7] Marstrand, J. M.: The dimension of Cartesian product sets. Proc. Camb. Philos. Soc. 50 198-202 (1954). | DOI | MR | Zbl
[8] Moran, P.: Additive functions of intervals and Hausdorff measure. Proc. Cambridge Philos. Soc. 42 15-23 (1946). | MR | Zbl
[9] Neunhäuserer, J.: Dimension theoretical properties of generalized Baker's transformations. Nonlinearity 15 1299-1307 (2002). | DOI | MR | Zbl
[10] Neunhäuserer, J.: Dimension Theory for Linear Solenoids. Fractals 15 63-72 (2007). | DOI | MR
[11] Pesin, Ya.: Dimension Theory in Dynamical Systems---Contemplary Views and Applications. University of Chicago Press (1997). | MR
[12] Smale, S.: Differentiable dynamical systems. Bull. Amer. Math. Soc. 73 747-817 (1967). | DOI | MR | Zbl
[13] Young, L.-S.: Dimension, entropy and Lyapunov exponents. Ergodic Theory Dyn. Syst. 2 109-124 (1982). | MR | Zbl
Cité par Sources :