分析了Barnsley M F的经典文献中递归仿射分形插值的数值模拟问题,利用Matlab与随机迭代算法,给出了递归仿射分形插值算例的随机迭代算法,得到相应分形插值曲线。递归仿射分形插值把较长的原像区间J_(i)′=[xl,xm]压缩映射到更短的像区...分析了Barnsley M F的经典文献中递归仿射分形插值的数值模拟问题,利用Matlab与随机迭代算法,给出了递归仿射分形插值算例的随机迭代算法,得到相应分形插值曲线。递归仿射分形插值把较长的原像区间J_(i)′=[xl,xm]压缩映射到更短的像区间J_(i)=[x_(i-1),x_(i)]时,有3种情况:(1)J_(i)■J_(i)′;(2)J_(i)■J_(i)′且J_(i)∩J_(i)′=Φ;(3)J_(i)J_(i)′,但是J_(i)∩J_(i)′≠Φ。根据递归仿射分形插值与分片分形插值,对以上3种情形进行了随机迭代数值模拟,给出了算法流程与详细的程序代码,这些数值分析是对分形插值理论的补充。最后,利用粒子群最优化算法给出仿射分形插值函数的盒维数最优解。展开更多
This paper presents a complete proof of a conjecture given by Ashwin, Deane and Fu that the map describing the dynamical behavior of the Sigma-Delta modulator has a global attractor. By viewing the map as a piecewise ...This paper presents a complete proof of a conjecture given by Ashwin, Deane and Fu that the map describing the dynamical behavior of the Sigma-Delta modulator has a global attractor. By viewing the map as a piecewise rotation, and by geometric analysis, the authors give a simpler and more sufficient proof of the conjecture, than the one presented by Deane and published in Dynamical Systems, 2002,17： 377 - 388.展开更多
In this paper, we discuss a class of piecewise linear hyperbolic maps on the 2-torus. These maps arise in the second-order digital fdter with two＇ s complement arithmetic. By introducing codings underlying the map op...In this paper, we discuss a class of piecewise linear hyperbolic maps on the 2-torus. These maps arise in the second-order digital fdter with two＇ s complement arithmetic. By introducing codings underlying the map operations, we give some admissibility conditions for symbolic sequences and find some periodic properties of these symbolic sequences. Then we use these conditions to check the admissibility of periodic symbol sequences.展开更多
In this paper,we discuss the invariant measures for planar piecewise isometries.It is shown that the Hausdorff measure restricted to an almost invariant set with respect to the Hausdorff measure is invariant.
文摘分析了Barnsley M F的经典文献中递归仿射分形插值的数值模拟问题,利用Matlab与随机迭代算法,给出了递归仿射分形插值算例的随机迭代算法,得到相应分形插值曲线。递归仿射分形插值把较长的原像区间J_(i)′=[xl,xm]压缩映射到更短的像区间J_(i)=[x_(i-1),x_(i)]时,有3种情况:(1)J_(i)■J_(i)′;(2)J_(i)■J_(i)′且J_(i)∩J_(i)′=Φ;(3)J_(i)J_(i)′,但是J_(i)∩J_(i)′≠Φ。根据递归仿射分形插值与分片分形插值,对以上3种情形进行了随机迭代数值模拟,给出了算法流程与详细的程序代码,这些数值分析是对分形插值理论的补充。最后,利用粒子群最优化算法给出仿射分形插值函数的盒维数最优解。
基金Project supported by Science Foundation of Shanghai Municipal Commission of Education （Grant No. 03AK33 ）, and National Natural Science Foundation of China （Grant No. 10471087）
文摘This paper presents a complete proof of a conjecture given by Ashwin, Deane and Fu that the map describing the dynamical behavior of the Sigma-Delta modulator has a global attractor. By viewing the map as a piecewise rotation, and by geometric analysis, the authors give a simpler and more sufficient proof of the conjecture, than the one presented by Deane and published in Dynamical Systems, 2002,17： 377 - 388.
基金Project supported by National Natural Science Foundation of Chi-na (Grant No .10471087) ,and Shanghai Municipal Commission ofEducation (Grant No .03AK33)
文摘In this paper, we discuss a class of piecewise linear hyperbolic maps on the 2-torus. These maps arise in the second-order digital fdter with two＇ s complement arithmetic. By introducing codings underlying the map operations, we give some admissibility conditions for symbolic sequences and find some periodic properties of these symbolic sequences. Then we use these conditions to check the admissibility of periodic symbol sequences.
基金Project supported by the National Natural Science Foundation of China (Grant No.10672146)the Natural Science Foundation of Jiangxi Province (Grant No.2007GQS0142)
文摘In this paper,we discuss the invariant measures for planar piecewise isometries.It is shown that the Hausdorff measure restricted to an almost invariant set with respect to the Hausdorff measure is invariant.
