报告题目：2014年复动力系统研讨会日程安排
报告人：数学测试
时间：2014-06-20
地点：
摘要：
2014年6月21日
上午
9:30-10:20 沈维孝（新加坡国立大学）
Title:On Lebesgue density points of Collet-Eckmann parameters.
10:30-11:20 王晓光 (浙江大学)
Title: Elliptic curves and complex dynamics.
下午
2:30-3:20 崔鸿飞（中国科学院武汉物理与数学研究所)
Title:Invariant measures and wandering intervals for contracting Lorenz maps.
3:30-4:20 玄祖兴（北京联合大学）
Title:Hyperbolic entire functions with bounded Fatou components.
4:30-5:20 褚海丰（西北大学）
Title:On the Blaschke Circle Diffeomorphisms.
2014年6月22日
上午
9:30-10:20 崔贵珍（中国科学院数学与系统科学研究院）
Title:Twist deformation of rational maps.
10:30-11:20 廖良文（南京大学）
Title:The complex differential and difference equations and their applications.
下午
2:30-3:20 李佑驹（北京大学）
Title:Thurston映射曲线在拉回映射下具有有限吸引子的一个充分条件.
3:30-4:20 张高飞（南京大学）
Title:Constructing rays for exponential maps with compact accumulation sets in the plane.
4:30-5:20 高 延（四川大学）
Title:A survey of the results about the core entropy of quadratic polynomials.
地点:数学院一楼报告厅
2014年复动力系统研讨会报告题目及摘要
Speaker: 沈维孝 （新加坡国立大学）
Title:On Lebesgue density points of Collet-Eckmann parameters
Abstract:I will give a brief historical account on generalizations and extensions of Jakobson' theorem on abundance of non-uniformly expanding interval maps. I will present a conjecture on Lebesgue density points of Collet-Eckmann parameters in the quadratic family and also discuss possible approach to this conjecture.
Speaker: 王晓光 (浙江大学)
Title: Elliptic curves and complex dynamics.
Abstract: We will review some well-known results on elliptic curves. Relations between the arithmetric properties of elliptic curves and the dynamical properties of Lattes maps are established. Besed on this relation, we give a dynamical proof of Masser-Zannier's finite theorem on Legendre elliptic curves. Joint work with Laura DeMarco and Hexi Ye.
Speaker: 崔鸿飞 (中国科学院武汉物理与数学研究所)
Title:Invariant measures and wandering intervals for contracting Lorenz maps
Abstract: For an interval map whose critical point set may contain critical points with different one-sided critical orders and jump discontinuities (e.g. contracting Lorenz maps), under a mild condition on critical orbits, we prove that it has an invariant probability measure which is absolutely continuous with respect to Lebesgue measure by using the methods of Bruin et al [Invent.Math. 172(3) (2008), 509–533], together with ideas from Nowicki and van Strien [Invent.Math. 105(1) (1991), 123–136]. We also show that it admits no wandering intervals.
Speaker: 玄祖兴 （北京联合大学）
Title:Hyperbolic entire functions with bounded Fatou components（written by Walter Bergweiler, NuriaFagella, Lasse Rempe-Gillen）
Abstract:In this talk, we will introduce some new results by Walter Bergweiler, NuriaFagella, LasseRempe-Gillen
Speaker: 褚海丰 （西北大学）
Title:On the Blaschke Circle Diffeomorphisms.
Abstract:Defined Blaschke family
If is an analytically linearizable element of the Blaschke family for some and , then the rotation number is a Brjuno number. Conversely, for every Brjuno number , there exist and such that is analytically linearizable and =.
Speaker: 崔贵珍 (中国科学院数学与系统科学研究院)
Title:Twist deformation of rational maps
Abstract. Consider the Riemann surfaces of a geometrically finite rational map. A repeated Dehn twistalong geodesics will produce a sequence of rational maps in its moduli space. We will prove that this sequenceis convergent under certain condition. The proof involves an iteration on Teichmuller spaces.
Speaker： 廖良文 （南京大学）
Title:The complex differential and difference equations and their applications.
Abstract:In this talk, we will present some new results about solving nonlinear
differential equations by using Wiman-Valiron theory and Nevanlinna theory in the valuedistributions of meromorphic functions, especially, Clunie lemma. We also prove thesome extend Hayman's theorems about differential polynomials. We discuss algebraicdifferential equations with admissible meromorphicsolutions.Furthermore, we discuss theuniqueness of the entire functions which share some value with their difference operatorsor derivatives.
Speaker: 李佑驹 （北京大学）
Title:Thurston映射曲线在拉回映射下具有有限吸引子的一个充分条件
Abstract:一族曲线（multicurve）在Thurston拉回映射下的动力性质的研究是一个很有趣的问题。2012年Pilgrim在文章《An algebraic formulation of Thurston's characterization of rational functions》中给出Thurston拉回映射具有有限全局吸引子的一个充分条件。我们将给出一个具有全局吸引子的更弱的条件并给出在此条件下找 出全局吸引子的一个算法。有例子表明用我们的条件可以知道可存在全局吸引子，而该例子不能用Pilgrim的条件得到具有全局吸引子
Speaker: 张高飞（南京大学）
Title:Constructing rays for exponential maps with compact accumulation sets in the plane.
Abstract:It is know that non-landing rays exist for exponential maps. The accumulation sets of all known examples for non-landing rays are indecomposable continuums in the sphere, which are not compact in the plane. In this work, we construct rays for certain exponential maps whose accumulation sets are arc segments in the plane.
Speaker: 高延 （四川大学）
Title: A survey of the results about the core entropy of quadratic polynomials
Abstract: I will give a summary of the recent development about the core entropy of complex quadratic polynomials, which is developed by Milnor, Thurston, Douady, Tiozzo…, and some related results.
