The bounds of the general M and J sets were analytically offered. Some of, the bounds were optimal in certain meaning. It not only solved the primary problem of the construction of fractal sets by escape time algorith...The bounds of the general M and J sets were analytically offered. Some of, the bounds were optimal in certain meaning. It not only solved the primary problem of the construction of fractal sets by escape time algorithm, and followed from the conclusion, but also offered two estimations of some special Julia set's Hausdorff's dimension by approximate linearization method.展开更多
We study Misiurewicz points on the parameter space about a family of rational maps Tλ concerning renormalization transformation in statistical mechanic. We determine the intersection points of the Julia set J(Tλ) an...We study Misiurewicz points on the parameter space about a family of rational maps Tλ concerning renormalization transformation in statistical mechanic. We determine the intersection points of the Julia set J(Tλ) and the positive real axis R+and discuss the continuity of the Hausdorff dimension HD(J(f)) about real parameter λ.展开更多
We prove that wandering components of the Julia set of a polynomial are singletons provided each critical point in a wandering Julia component is non-recurrent. This means a conjecture of Branner-Hubbard is true for t...We prove that wandering components of the Julia set of a polynomial are singletons provided each critical point in a wandering Julia component is non-recurrent. This means a conjecture of Branner-Hubbard is true for this kind of polynomials.展开更多
文摘The bounds of the general M and J sets were analytically offered. Some of, the bounds were optimal in certain meaning. It not only solved the primary problem of the construction of fractal sets by escape time algorithm, and followed from the conclusion, but also offered two estimations of some special Julia set's Hausdorff's dimension by approximate linearization method.
基金supported by National Natural Science Foundation of China(GrantNos.11371363,11231009,11261002 and 11201474)the Special Basic Scientific Research Funds of Central Universities in China
文摘We study Misiurewicz points on the parameter space about a family of rational maps Tλ concerning renormalization transformation in statistical mechanic. We determine the intersection points of the Julia set J(Tλ) and the positive real axis R+and discuss the continuity of the Hausdorff dimension HD(J(f)) about real parameter λ.
基金The work was done during the author's visit to Morningside Mathematical Centre ofChinese Academy of Sciences. He thanks all members in the seminar on complex dynamics at Beijing and referees for some corrections and language comments. This work was par
文摘We prove that wandering components of the Julia set of a polynomial are singletons provided each critical point in a wandering Julia component is non-recurrent. This means a conjecture of Branner-Hubbard is true for this kind of polynomials.
基金Supported by the National Natural Science Foundation of China under Grant No.69878038 (国家自然科学基金) the Assisting Project of Ministry of Education of China for Backbone Teachers of University and College (国家教育部高等学校骨干教师资助计划)
