Some New Concepts of Dimension
作者： Józef Myjak
DOI: 10.1007/978-3-7643-8482-1_25
关键词: Hausdorff space 、 Mathematics 、 Algebra 、 Variational principle 、 Dimension (graph theory) 、 Differential equation 、 Fractal 、 Iterated function system 、 Generic property
摘要: This paper contains a review of recent results concerning some new concepts analytical dimensions sets and measures. We make in evidence the relationship between these classical once. In particular we give estimates, variational principles generic properties. Finally, applications theory iterated function systems differential equations.
springer.com
sci-hub.st 参考文章(43)
Ya. B. Pesin, Dimension theory in dynamical systems ,(1997)
Józef Myjak, Tomasz Szarek, A Lower Estimation of the Hausdorff Dimension for Attractors with Overlaps Journal of Statistical Physics. ,vol. 105, pp. 649- 657 ,(2001) , 10.1023/A:1012231910484
A. Lasota, J. Myjak, On a dimension of measures Bulletin of The Polish Academy of Sciences Mathematics. ,vol. 50, pp. 221- 235 ,(2002)
Yakov B. Pesin, Dimension Theory in Dynamical Systems: Contemporary Views and Applications University of Chicago Press. ,(1997) , 10.7208/9780226662237
Boris Solomyak, Károly Simon, Correlation dimension for self-similar Cantor sets with overlaps Fundamenta Mathematicae. ,vol. 155, pp. 293- 300 ,(1998)
A. Lasota, J. Myjak, Semifractals on Polish spaces Bulletin of The Polish Academy of Sciences Mathematics. ,vol. 46, pp. 179- 196 ,(1998)
Józef Myjak, Ryszard Rudnicki, Typical properties of correlation dimension. Real analysis exchange. ,vol. 28, pp. 269- 278 ,(2003) , 10.14321/REALANALEXCH.28.2.0269
Wai Chin, Brian Hunt, James A. Yorke, Correlation dimension for iterated function systems Transactions of the American Mathematical Society. ,vol. 349, pp. 1783- 1796 ,(1997) , 10.1090/S0002-9947-97-01900-4
Genyuk, A Typical Measure Typically Has No Local Dimension Real analysis exchange. ,vol. 23, pp. 525- 538 ,(1997) , 10.2307/44153978
Itamar Procaccia, Peter Grassberger, H. G. E. Hentschel, On the characterization of chaotic motions Dynamical System and Chaos. ,vol. 179, pp. 212- 222 ,(1983) , 10.1007/3-540-12276-1_18