| 1. | The second result is on the local connectivity of the julia set of fc in its dynamical plane . we obtain theorem 2
我们得到的第二个结论是关于动力学平面上人的julia集的局部连通性：定理2 |
| 2. | / / the julia set j ( fc ) of fc is connected , then the boundary of the immediately attracting domain of fc at 0 is a jordan curve
L 。 a集是连通的，那么人在0 ，卢、的直接吸引域是joulan曲线，从而是局部连通的。 |
| 3. | With the similar technique , they gave a complete description of the connectivity and the totally disconnectivity of the julia sets of cubic polynomials
他们用类似的拼图技巧，对三次多项式的julia集的连通性和完全不连通性作出了完整的描述。 |
| 4. | A further application of the puzzle theory , due to faught and hubbard , is the study of the julia sets and the connectedness locus of a cubic family with one critical fixed point
利用这个理论， faught和hubbard研究了有临界不动点的单参数三次多项式族的julia集及其连通迹的局部连通性。 |
| 5. | In fact , the curve is a fractal curve . lastly , with computer experiments and julia set in broad sense , the design of the pattern of various arts can be realized . fictional nature sights appear by compounding each single picture
最后，用julia集的思想实现了多幅艺术图案的设计与绘制，并将绘制的多种分形图进行了综合运用，实现了虚拟景观的生成。 |
| 6. | In the case ( 3 ) . we also have that each critical component and its inverse images under iterations are homeomorphic to the filled julia set of a quadratic polynomial with connected julia set . each of the other components of a ' ( / ) is a single point
对于（ 3 ） ，我们进一步有：填充juia集包含临界点的周期分支及其迭代逆象同胚于一个有连通julia集的二次多项式的填充julia集，而其他分支都是单点。 |
| 7. | Yoccoz introduced a powerful puzzle technique and obtained the result that if the quadratic polynomial pc ( z ) with , which has no indifferent cycle , is not infinitely renormalizable , then the julia set j ( pc ) of pc is locally connected while dm is also locally connected at c
利用这个技巧，他得到了对c m ，如果二次多项式pc ( z )不是无穷可重整化的，并且没有抛物周期点，那么julia集j ( pc )是局部连通的，并且m在c也是局部连通的。 |
| 8. | At the end of the last century , c . j . yoccoz is made significant contributions to the theory of complex dynamics , one of which is the study of the local connectivity of the julia sets of quadratic polynomials pc ( z ) = z2 + c and the mandelbrot set m . in his work
C yoccoz对复动力系统理论作出了重要的贡献，其中之一就是对二次多项式pc ( z ) = z ~ 2 + c的julia集和mandelbrot集m的局部连通性的研究。在他的工作中， yoccoz引进了一种强有力的方法? ?拼图技巧。 |
| 9. | If fc has no parabolic periodic points and is not renormalizable , then j ( fc ] is locally connected . here fc is renormalizable if there are simply connected domains u and u " and a positive integer n such that contains the critical point c or - c1 and is a quadratic - like mapping with connected julia set
这里， it称为可重整化的定义为：存在单连通区域l ’ 、 u ’及正整数n ；使得i ’ u ，仁’包含临界点c或一c ， ” ： r一u是一个二层分支覆盖，且拟共形共轭于一个有连通julia集的二次多项式。 |
| 10. | Let f be a biquadratic polynomial , then ( 1 ) the julia set of f is connected if and only if the orbits of all critical pionts are bounded ; ( 2 ) the julia set of f is totally disconnected if and only if every connected component of the filled julia set of f containing critical points is not periodic under iterations : ( 3 ) if f does not satisfy the conditions ( 1 ) and ( 2 ) , then the julia set of f has infinitely many non - trivial connected components , where a component is trivial if it contains only one point
A集是完全不连通的当且仅当f的任何临界声、不属于填充julm集的周期分支内。你当j的临界卢、不满足条件小， ” j时， f的几ha集有可数个非平凡的连通分支，这里，一个分支是平凡的，如果它仅由一个卢、组成。 。 |
