标题： 三次多项式参数空间中的抛物线爆裂 显示英文标题

标题： Parabolic Implosion in the Parameter Space of Cubic Polynomials

摘要： 抛物线爆炸描述了当一个抛物线不动点被扰动时，Julia集的丰富性。 在参数空间中研究抛物线爆炸也是自然的。 特别是，当适当扰动具有稳定抛物线不动点的三次多项式族到附近的族时，分岔loci的丰富性会发生。 我们研究三次多项式参数空间中这种丰富性的拓扑结构，并将其与二次多项式对应的Julia集的丰富性联系起来，后者在80年代已被P. Lavaurs系统地研究过。 显示英文摘要

摘要： Parabolic implosion describes the enrichment of Julia sets when a parabolic fixed point is perturbed. It is also natural to study parabolic implosion in parameter spaces. In particular, when one perturbs properly the family of cubic polynomials having a stable parabolic fixed point into nearby families, the enrichment of the bifurcation loci occurs. We investigate the topology of such enrichment in the parameter space of cubic polynomials and relate it to the corresponding enrichment of Julia sets of quadratic polynomials, the latter of which has been studied systematically by P. Lavaurs in the 80s.