[Analyse fractale des trajectoires spirales de quelques champs de vecteurs dans ]
We study box dimension and Minkowski content of spiral solutions of some dynamical systems in .
Nous étudions la ‘box dimension’ et le contenu de Minkowski des solutions spirales de quelques systèmes dynamiques dans .
Accepté le :
Publié le :
Žubrinić, Darko 1 ; Županović, Vesna 1
@article{CRMATH_2006__342_12_959_0,
author = {\v{Z}ubrini\'c, Darko and \v{Z}upanovi\'c, Vesna},
title = {Fractal analysis of spiral trajectories of some vector fields in $ {\mathbb{R}}^{3}$},
journal = {Comptes Rendus. Math\'ematique},
pages = {959--963},
year = {2006},
publisher = {Elsevier},
volume = {342},
number = {12},
doi = {10.1016/j.crma.2006.04.021},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.crma.2006.04.021/}
}
TY - JOUR
AU - Žubrinić, Darko
AU - Županović, Vesna
TI - Fractal analysis of spiral trajectories of some vector fields in $ {\mathbb{R}}^{3}$
JO - Comptes Rendus. Mathématique
PY - 2006
SP - 959
EP - 963
VL - 342
IS - 12
PB - Elsevier
UR - https://www.numdam.org/articles/10.1016/j.crma.2006.04.021/
DO - 10.1016/j.crma.2006.04.021
LA - en
ID - CRMATH_2006__342_12_959_0
ER -
%0 Journal Article
%A Žubrinić, Darko
%A Županović, Vesna
%T Fractal analysis of spiral trajectories of some vector fields in $ {\mathbb{R}}^{3}$
%J Comptes Rendus. Mathématique
%D 2006
%P 959-963
%V 342
%N 12
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.crma.2006.04.021/
%R 10.1016/j.crma.2006.04.021
%G en
%F CRMATH_2006__342_12_959_0
Žubrinić, Darko; Županović, Vesna. Fractal analysis of spiral trajectories of some vector fields in $ {\mathbb{R}}^{3}$. Comptes Rendus. Mathématique, Tome 342 (2006) no. 12, pp. 959-963. doi: 10.1016/j.crma.2006.04.021
[1] Hopf–Takens bifurcations and centers, J. Differential Equations, Volume 202 (2004) no. 1, pp. 1-31
[2] Generalized Liénard equations, cyclicity and Hopf–Takens bifurcations, Qualitative Theory of Dynamical Systems, Volume 6 (2005), pp. 195-222
[3] Dimension de spirales, Bull. Soc. Math. France, Volume 111 (1983), pp. 193-201
[4] Measure Theory and Fine Properties of Functions, CRC Press, 1992
[5] Fractal Geometry, John Wiley and Sons, 1990
[6] Tubes, Addison-Wesley, 1990
[7] Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, 1983
[8] Generalized Minkowski content, spectrum of fractal drums, fractal strings and the Riemann zeta-function, Mem. Amer. Math. Soc., Volume 127 (1997) no. 608
[9] Maximally singular Sobolev functions, J. Math. Anal. Appl., Volume 304 (2005) no. 2, pp. 531-541
[10] The Riemann zeta-function and the one-dimensional Weyl–Berry conjecture for fractal drums, Proc. London Math. Soc. (3), Volume 66 (1993) no. 1, pp. 41-69
[11] Geometry of Sets and Measures in Euclidean Spaces. Fractals and Rectifiability, Cambridge Univ. Press, Cambridge, 1995
[12] Minkowski–Bouligand dimension of solutions of the one-dimensional p-Laplacian, J. Differential Equations, Volume 190 (2003), pp. 268-305
[13] Some metric-singular properties of the graph of solutions of the one-dimensional p-Laplacian, Electronic J. Differential Equations, Volume 2004 (2004) no. 60, pp. 1-25
[14] Unfoldings of certain singularities of vector fields: Generalized Hopf bifurcations, J. Differential Equations, Volume 14 (1973), pp. 476-493
[15] Curves and Fractal Dimension, Springer-Verlag, 1995
[16] Singular sets of Sobolev functions, C. R. Acad. Sci. Paris, Ser. I, Volume 334 (2002), pp. 539-544
[17] Singular sets of Lebesgue integrable functions, Chaos, Solitons, Fractals, Volume 21 (2004), pp. 1281-1287
[18] D. Žubrinić, Analysis of Minkowski contents of fractal sets and applications Real Anal. Exchange, in press
[19] Fractal analysis of spiral trajectories of some planar vector fields, Bull. Sci. Math., Volume 129 (2005) no. 6, pp. 457-485
[20] D. Žubrinić, V. Županović, Box dimension of spiral trajectories of some vector fields in , preprint
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