In 1992, Branner and Hubbard raised a conjecture that the Julia set of a polynomial is a Cantor set if and only if each critical component of its filled-in Julia set is not periodic. This conjecture was solved recentl...In 1992, Branner and Hubbard raised a conjecture that the Julia set of a polynomial is a Cantor set if and only if each critical component of its filled-in Julia set is not periodic. This conjecture was solved recently. In this paper, we generalize this result to a class of rational functions.展开更多
By means of the Branner-Hubbard puzzle, the author studies the topology of filled-in Julia sets for geometrically finite polynomials,and proves a conjecture of C. McMullen and a conjecture of B. Branner and J. H. Hu...By means of the Branner-Hubbard puzzle, the author studies the topology of filled-in Julia sets for geometrically finite polynomials,and proves a conjecture of C. McMullen and a conjecture of B. Branner and J. H. Hubbard partially.展开更多
文摘In 1992, Branner and Hubbard raised a conjecture that the Julia set of a polynomial is a Cantor set if and only if each critical component of its filled-in Julia set is not periodic. This conjecture was solved recently. In this paper, we generalize this result to a class of rational functions.
文摘By means of the Branner-Hubbard puzzle, the author studies the topology of filled-in Julia sets for geometrically finite polynomials,and proves a conjecture of C. McMullen and a conjecture of B. Branner and J. H. Hubbard partially.
