Iterated function systems （IFS） were introduced by Hutchinson in 1981 as a natural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahu and A. Chakraborty introduced K-Iterated Function...Iterated function systems （IFS） were introduced by Hutchinson in 1981 as a natural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahu and A. Chakraborty introduced K-Iterated Function System using Kannan mapping which would cover a larger range of mappings. In this paper, following Hutchinson, D. R. Sahu and A. Chakraborty, we present some new iterated function systems by using the so-called generalized contractive mappings, which will also cover a large range of mappings. Our purpose is to prove the existence and uniqueness of attractors for such class of iterated function systems by virtue of a Banach-like fixed point theorem concerning generalized contractive mappings.展开更多
In this paper, we present some fixed point theorems of iterated function systems consisting of α-ψ-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function s...In this paper, we present some fixed point theorems of iterated function systems consisting of α-ψ-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function systems consisting of Banach contractive mappings in Fractal space constituted by the compact subset of generalized metric space, which is Mso extensively applied in topological dynamic system.展开更多
Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, th...Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach.展开更多
This paper gives the definition of fractal affine transformation and presents a specific method for its realization and its corresponding mathematical equations which are essential in fractal image construction.
The problems of determining the spectrality or non-spectrality of a measure have been received much attention in recent years. One of the non-spectral problems on <span style="white-space:nowrap;"><...The problems of determining the spectrality or non-spectrality of a measure have been received much attention in recent years. One of the non-spectral problems on <span style="white-space:nowrap;"><em>μ<sub>M,D</sub></em></span><sub> </sub>is to estimate the number of orthogonal exponentials in <em>L</em><sup>2</sup><span style="white-space:normal;">(</span><em>μ<sub>M,D<span style="white-space:normal;">)</span></sub></em>. In the present paper, we establish some relations inside the zero set <img src="Edit_2196df81-d10f-4105-a2a9-779f454a56c3.png" width="55" height="23" alt="" /> by the Fourier transform of the self-affine measure <em>μ<sub>M,D</sub></em>. Based on these facts, we show that <em>μ<sub>M,D</sub></em> is a non-spectral measure<em><sub> </sub></em>and there exist at most 4 mutually orthogonal exponential functions in <em style="white-space:normal;"><em style="white-space:normal;">L</em><sup style="white-space:normal;">2</sup><span style="white-space:normal;">(</span><span style="white-space:normal;"></span><em style="white-space:normal;">μ<sub>M,D)</sub></em></em>, where the number 4 is the best possible. This extends several known conclusions.展开更多
基金Partially supported by National Natural Science Foundation of China (No. 10961003)
文摘Iterated function systems （IFS） were introduced by Hutchinson in 1981 as a natural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahu and A. Chakraborty introduced K-Iterated Function System using Kannan mapping which would cover a larger range of mappings. In this paper, following Hutchinson, D. R. Sahu and A. Chakraborty, we present some new iterated function systems by using the so-called generalized contractive mappings, which will also cover a large range of mappings. Our purpose is to prove the existence and uniqueness of attractors for such class of iterated function systems by virtue of a Banach-like fixed point theorem concerning generalized contractive mappings.
基金The NSF(11271150)of ChinaChina Government Scholarship
文摘In this paper, we present some fixed point theorems of iterated function systems consisting of α-ψ-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function systems consisting of Banach contractive mappings in Fractal space constituted by the compact subset of generalized metric space, which is Mso extensively applied in topological dynamic system.
文摘Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach.
文摘This paper gives the definition of fractal affine transformation and presents a specific method for its realization and its corresponding mathematical equations which are essential in fractal image construction.
文摘The problems of determining the spectrality or non-spectrality of a measure have been received much attention in recent years. One of the non-spectral problems on <span style="white-space:nowrap;"><em>μ<sub>M,D</sub></em></span><sub> </sub>is to estimate the number of orthogonal exponentials in <em>L</em><sup>2</sup><span style="white-space:normal;">(</span><em>μ<sub>M,D<span style="white-space:normal;">)</span></sub></em>. In the present paper, we establish some relations inside the zero set <img src="Edit_2196df81-d10f-4105-a2a9-779f454a56c3.png" width="55" height="23" alt="" /> by the Fourier transform of the self-affine measure <em>μ<sub>M,D</sub></em>. Based on these facts, we show that <em>μ<sub>M,D</sub></em> is a non-spectral measure<em><sub> </sub></em>and there exist at most 4 mutually orthogonal exponential functions in <em style="white-space:normal;"><em style="white-space:normal;">L</em><sup style="white-space:normal;">2</sup><span style="white-space:normal;">(</span><span style="white-space:normal;"></span><em style="white-space:normal;">μ<sub>M,D)</sub></em></em>, where the number 4 is the best possible. This extends several known conclusions.
