engleski

From singular dimensions and fractal analysis of vector fields to Lapidus zeta functions

The talk will be concentrated on some problems of fractal analysis appearing in several areas of Mathematics. It will consist of three parts, as indicated in the title. The first part will be dedicated to the study of the “wildest” possible functions from a given space of real functions, as well as to the “wildest” weak solutions corresponding to a given class of elliptic boundary value problems. We achieve this by the simultaneous use of the Hausdorff and box (or Minkowski) dimensions. In the second part, we shall provide a brief sketch of the joint work initiated by Vesna Županović, University of Zagreb, dealing with fractal analysis of vector fields, including the Hopf-Takens bifurcation. The third part of the talk will present a short survey of the higher-dimensional theory of complex dimensions, initiated in 2009 by Michel L. Lapidus, University of California, Riverside, developed over the past seven years of our joint work, together with Goran Radunović, University of Zagreb. More details about our current work can be found on the web pages of the Centre for Nonlinear Dynamics, Zagreb: www.math.hr/cnd. We express our gratitude to the Croatian Science Foundation for its support of the project IP-2014-09-2285. References: M. L. Lapidus, G. Radunović and D. Žubrinić, Fractal zeta functions and complex dimensions of relative fractal drums, J. Fixed Point Theory and Appl. No. 2, 15 (2014), 321–378. Festschrift issue in honor of Haim Brezis’ 70th birthday. (DOI: 10.1007/s11784-014-0207-y.) (Also: e-print, arXiv:1407.8094v3 [math-ph], 2014.) M. L. Lapidus, G. Radunović and D. Žubrinić, Fractal Zeta Functions and Fractal Drums: Higher-Dimensional Theory of Complex Dimensions, research monograph, Springer, New York, 2016, to appear, approx. 660 pages.

singular dimension; Minkowski dimension; Hopf-Takens bifurcation; complex dimension; Lappidus zeta function

nije evidentirano