Results 291 to 300 of about 957,336 (307)
On the box dimension of an invariant set [PDF]
Nonlinearity, 2000 This paper is devoted to the dimension of a general forward invariant set of a \(C^1\)-diffeomorphism in \(\mathbb{R}^n\) where it is only assumed that the diffeomorphism is volume increasing near the forward invariant set. The author gives a simple proof of upper bound for the box dimension of a forward invariant set of a \(C^1\)-diffeomorphism of ...
openaire +2 more sources
Some of the next articles are maybe not open access.
Related searches:
Related searches:
BOX DIMENSION AND MINKOWSKI CONTENT OF THE CLOTHOID
Fractals, 2009We prove that the box dimension of the standard clothoid is equal to d = 4/3. Furthermore, this curve is Minkowski measurable, and we compute its d-dimensional Minkowski content. Oscillatory dimensions of component functions of the clothoid are also equal to 4/3.
Luka Korkut +2 more
openaire +3 more sources
On the performance of box-counting estimators of fractal dimension [PDF]
Biometrika, 1993 Summary: Box-counting estimators are popular for estimating fractal dimension. However, very little is known of their stochastic properties, despite increasing statistical interest in their application. We show that, if the irregular curve to which the estimators are applied is modelled by a Gaussian process, concise formulae may be developed for ...
Andrew T. A. Wood, Peter Hall
openaire +1 more source
Box and packing dimensions of projections and dimension profiles
Mathematical Proceedings of the Cambridge Philosophical Society, 2001For E a subset of ℝn and s ∈ [0, n] we define upper and lower box dimension profiles, B-dimsE and B-dimsE respectively, that are closely related to the box dimensions of the orthogonal projections of E onto subspaces of ℝn. In particular, the projection of E onto almost all m-dimensional subspaces has upper box dimension B-dimmE and lower box ...
openaire +3 more sources
Projection theorems for box and packing dimensions
Mathematical Proceedings of the Cambridge Philosophical Society, 1996AbstractWe show that if E is an analytic subset of ℝn thenfor almost all m–dimensional subspaces V of ℝn, where projvE is the orthogonal projection of E onto V and dimp denotes packing dimension. The same inequality holds for lower and upper box counting dimensions, and these inequalities are the best possible ones.
Kenneth J. Falconer, J. D. Howroyd
openaire +2 more sources
Topological and Box Counting Dimensions [PDF]
, 2020 A mind once stretched by a new idea never regains its original dimension. Oliver Wendell Holmes, Jr. (1841–1935), American, U.S. Supreme Court justice from 1902 to 1932.
openaire +1 more source
Box dimension of Neimark–Sacker bifurcation
Journal of Difference Equations and Applications, 2014In this paper we show how a change of a box dimension of orbits of two-dimensional discrete dynamical systems is connected to their bifurcations in a nonhyperbolic fixed point. This connection is already shown in the case of one-dimensional discrete dynamical systems and Hopf bifurcation for continuous systems.
openaire +4 more sources
The Hausdorff and box dimension of fractals with disjoint projections in two dimensions [PDF]
Glasgow Mathematical Journal, 2002 In this paper, we obtain an exact formula for the Hausdorff and box dimensions of a class of self-affine sets in two dimensions, namely those with disjoint projections. We prove, in particular, that fractals in this class have a Hausdorff and box dimension that is equal to the maximum Hausdorff and box dimension of one of their projections.
openaire +2 more sources
2019
The main goal of this chapter is to generalize the classical box dimension in the broader context of fractal structures. We state that whether the so-called natural fractal structure (which any Euclidean subset can be always endowed with) is selected, then the box dimension remains as a particular case of the generalized fractal dimension models.
Manuel Fernández-Martínez +3 more
openaire +2 more sources
The main goal of this chapter is to generalize the classical box dimension in the broader context of fractal structures. We state that whether the so-called natural fractal structure (which any Euclidean subset can be always endowed with) is selected, then the box dimension remains as a particular case of the generalized fractal dimension models.
Manuel Fernández-Martínez +3 more
openaire +2 more sources
Computing the Box Counting Dimension
2020From roughly the late 1980s to the mid-1990s, a very large number of papers studied computational issues in determining fractal dimensions of geometric objects, or provided variants of algorithms for calculating the fractal dimensions, or applied these techniques to real-world problems.
openaire +2 more sources