Box dimension of spiral trajectories of some vector fields in ℝ3

被引：0
作者：
Žubrinić D. [1 ]
Županović V. [1 ]
机构：
[1] University of Zagreb, 10000 Zagreb
来源：
Qualitative Theory of Dynamical Systems | 2005年 / 6卷 / 2期
关键词：
Bi-Lipschitz mapping; Box dimension; Minkowski content; Spiral; Vector field;
D O I：
10.1007/BF02972676
中图分类号：
学科分类号：
摘要：
We study the behaviour of Minkowski content of bounded sets under bi- Lipschitzian mappings. Applications include Minkowski contents and box dimensions of spirals in ℝ3, dynamical systems, and singular integrals.
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页码：251 / 272
页数：21
相关论文
共 21 条
  • [1] Caubergh M., Dumortier F., Hopf-Takens bifurcations and centers, J. Differential Equations, 202, 1, pp. 1-31, (2004)
  • [2] Caubergh M., Francoise J.P., Generalized Liénard equations, cyclicity and Hopf-Takens bifurcations, Qualitative Theory of Dynamical Systems, 6, pp. 195-222, (2005)
  • [3] Dupain Y., Mendes France M., Tricot C., Dimension de spirales, Bull. Soc. Math. France, 111, pp. 193-201, (1983)
  • [4] Evans L.C., Gariepy R.F., Measure theory and fine properties of functions, (1992)
  • [5] Falconer K., Fractal Geometry, (1990)
  • [6] Gray A., Tubes, (1990)
  • [7] Guckenheimer J., Holmes P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, (1983)
  • [8] He C.Q., Lapidus M.L., Generalized Minkowski content, spectrum of fractal drums, fractal strings and the Riemann zeta-function, Mem. Amer. Math. Soc, 127, 608, (1997)
  • [9] Horvat L., Zubrinic D., Maximally singular Sobolev functions, J. Math. Anal. Appl, 304, 2, pp. 531-541, (2005)
  • [10] Lapidus M., van Frankenhuysen M., Fractal Geometry and Number Theory. Complex dimensions of fractal strings and zeros of zeta functions, (2000)
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