Results 11 to 20 of about 1,343,845 (245)
Energy-optimal steering of transitions through a fractal basin boundary. [PDF]
, 2004 We study fluctuational transitions in a discrete dy- namical system having two co-existing attractors in phase space, separated by a fractal basin boundary. It is shown that transitions occur via a unique ac- cessible point on the boundary.
Luchinsky, D. G. +3 more
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Exact dimensionality and projections of random self-similar measures and sets [PDF]
, 2014 We study the geometric properties of random multiplicative cascade measures defined on self-similar sets. We show that such measures and their projections and sections are almost surely exact dimensional, generalizing a result of Feng and Hu's for self ...
Jin, Xiong +4 more
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A commutative noncommutative fractal geometry [PDF]
, 2010 In this thesis examples of spectral triples, which represent fractal sets, are examined and new insights into their noncommutative geometries are obtained.
Samuel, Tony; id_orcid +6 more
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The geometry of self-affine fractals [PDF]
, 2008 In this thesis we study the dimension theory of self-affine sets. We begin by introducing a number of notions from fractal geometry, in particular, dimensions, measure properties and iterated functions systems.
Miao, Jun Jie
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Analogues to Lie Method and Noether’s Theorem in Fractal Calculus
Fractal and Fractional, 2019 In this manuscript, we study symmetries of fractal differential equations. We show that using symmetry properties, one of the solutions can map to another solution.
Alireza Khalili Golmankhaneh +1 more
doaj +1 more source
Fractal and Fractional, 2019 In this paper, we give difference equations on fractal sets and their corresponding fractal differential equations. An analogue of the classical Euler method in fractal calculus is defined. This fractal Euler method presets a numerical method for solving
Alireza Khalili Golmankhaneh +1 more
doaj +1 more source
Estimation of the Fractal Dimensions of the Linear Combination of Continuous Functions
Mathematics, 2022 In the present paper, we try to estimate the fractal dimensions of the linear combination of continuous functions with different fractal dimensions.
Binyan Yu, Yongshun Liang
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New Properties and Sets Derived from the
Fractal and Fractional, 2023 Due to their practicality and convenient parametrization, fractals derived from iterated function systems (IFSs) constitute powerful tools widely used to model natural and synthetic shapes.
Mario A. Aguirre-López +2 more
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On the Fractional-Order Complex Cosine Map: Fractal Analysis, Julia Set Control and Synchronization
Mathematics, 2023 In this paper, we introduce a generalized complex discrete fractional-order cosine map. Dynamical analysis of the proposed complex fractional order map is examined. The existence and stability characteristics of the map’s fixed points are explored.
A. A. Elsadany +3 more
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New Derivatives on the Fractal Subset of Real-Line
Entropy, 2016 In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets.
Alireza Khalili Golmankhaneh +1 more
doaj +1 more source