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Mappings of Finite Distortion:¶Discreteness and Openness
Archive for Rational Mechanics and Analysis, 2001Let \(\Omega \subset \mathbb{R}^n, n\geq 2,\) be a bounded domain. A mapping \(f: \Omega \to \mathbb{R}^n\) in \(W^{1,1}(\Omega)\) is said to have a finite distortion if there exists a measurable function \(K(x)\geq 1\) such that \[ |Df(x)|\leq K(x) J(x,f) \quad\text{a.e.} \] These maps are currently under intensive research by many authors including ...
Kauhanen, Janne +2 more
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Comparisons of Typical Discrete Logistic Map and Henon Map
2014Applying chaos theory to the encryption scheme has become a hot spot. Although lots of chaotic maps have been proposed, they don’t have advantages in all respects. In this paper, the typical one-dimensional Logistic map and two-dimensional Henon map are studied.
Bingbing Song, Qun Ding
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Quasiregular Mappings and Discrete Group Actions
Journal of Mathematical Sciences, 2021We develop a new tool based on quasiconformal dynamics and conformal dynamics of discrete group actions in 3-geometries to construct new types of quasiregular and quasisymmetric mappings in space. This tool has close relations to new effects in Teichmüller spaces of conformally flat structures on closed hyperbolic 3-manifolds/orbifolds and non-trivial ...
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1983
In this chapter we shall deal with discrete noisy maps, which we got to know in the introduction. In the first sections of the present chapter we shall study in how far we can extend previous results on differential equations to such maps. In Sects. 7.7–7.9 we showed how the slaving principle can be extended.
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In this chapter we shall deal with discrete noisy maps, which we got to know in the introduction. In the first sections of the present chapter we shall study in how far we can extend previous results on differential equations to such maps. In Sects. 7.7–7.9 we showed how the slaving principle can be extended.
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2016
In this chapter we introduce definitions of maps, which are discrete surfaces obtained by gluing polygons along their sides, and we define generating functions to count them. We also derive Tutte’s equations, which are recursive equations satisfied by the generating functions.
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In this chapter we introduce definitions of maps, which are discrete surfaces obtained by gluing polygons along their sides, and we define generating functions to count them. We also derive Tutte’s equations, which are recursive equations satisfied by the generating functions.
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New Discrete Chaotic Multiplicative Maps Based on the Logistic Map
International Journal of Bifurcation and Chaos, 2018Chaos is a phenomenon which cannot be predicted if it manifests itself in a nonlinear system. Simple deterministic models, such as the logistic map [Formula: see text], are constructed to capture the essence of processes observed in nature. They are interesting also from a mathematical point of view: nonlinear models can behave in chaotic and ...
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Mapping the Continuous to the Discrete
2012This research proposes to explore the consequences of a phenomenological approach on designing for the aesthetics of interaction. Highly complex products in a ‘digital’ world, enlisting complex functions, hierarchies, system architectures, procedures and so on, are designed to be used by humans.
Stienstra, J.T. +4 more
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A higher dimensional chaotic map with discrete memristor
AEU - International Journal of Electronics and Communications, 2021Shaobo He, Yuexi Peng, Kehui Sun
exaly