Visitors
(来访时间: 2019年10月21日--25日)
- 报告: The dynamics of flipped alpha-continued fractions (2019年10月24日，上午 09:00--09:50， 数学楼401室)
- 摘要：In this talk we consider a family of continued fraction transformations that can be considered as a natural counterpart to the famous
Nakada's alpha-continued fraction maps, called flipped alpha-continued fractions. For this family we analyse the matching behaviour, which is a dynamical
phenomenon observed in various families of one-dimensional systems. We show that this family has Lebesgue almost everywhere matching, which is the first time
this has been observed in the setting of infinite measure ergodic theory. Then we use matching to obtain various ergodic properties of
the systems, such as their natural extension, an expression for the absolutely continuous invariant measure and the value of their Krengel entropy.
(来访时间: 2019年10月21日--24日)
- 报告: Univoque bases of real numbers: local dimension, Devil's staircase and isolated points (2019年10月24日，上午 10:00--10:50， 数学楼401室)
- 摘要： Given a positive integer $M$ and a real number $x>0$, let $\ub(x)$ be the set of all bases $q\in(1, M+1]$ for which there exists a unique sequence $(d_i)=d_1d_2\ldots$
with each digit $d_i\in\set{0,1,\ldots, M}$ satisfying
\[
x=\sum_{i=1}^\f\frac{d_i}{q^i}.
\]
The sequence $(d_i)$ is called a \emph{$q$-expansion} of $x$.
In this paper we investigate the local dimension of $\ub(x)$ and prove a `variation principle' for unique non-integer base expansions. We also determine the critical values of $\ub(x)$
that when $x$ passes the first critical value the set $\ub(x)$ changes from a set with positive Hausdorff dimension to a countable set, and when $x$ passes the second critical value
the set $\ub(x)$ changes from an infinite set to a singleton. Denote by $\us(x)$ the set of all unique $q$-expansions of $x$ for $q\in\ub(x)$. We give the Hausdorff dimension of
$\us(x)$ and show that the dimensional function $x\mapsto\dim_H\us(x)$ is a non-increasing Devil's staircase. Finally, we investigate the topological structure of $\ub(x)$. In
contrast with $x=1$ that $\ub(1)$ has no isolated points, we prove that for typical $x>0$ the set $\ub(x)$ contains isolated points.
(来访时间: 2019年4月11日)
- 报告: Introduction to Mobius Linear Disjointness (2019年4月11日，下午 15:00--16:00， 闵行数学楼401室)
- 摘要： The study of Mobius linear disjointness has gained much attention in recent several years. In this talk I will give an introduction to it,
I will also talk about some recent progress based on my joint works with my coauthors.
(来访时间: 2019年4月8日--10日)
- 报告: Local dimension of univoque bases (2019年4月10日，上午 10:00--11:45， 闵行3教306室)
- 摘要：Fix an alphabet A={0,1,…,M}. The univoque set U of bases q in (1,M+1) in which the number 1 has a unique expansion over the alphabet A
has been well studied. It has Lebesgue measure zero but Hausdorff dimension one. In this talk we will describe how the set U is distributed over the
interval (1,M+1) by determining the local dimension of U. As an application we give
a complete answer to a question of [P. Allaart, Adv. Math., 308:575--598, 2017] about strongly univoque sets. This is a joint work with Pieter Allaart.
Dejun Feng (丰德军) ： 香港中文大学数学系
(来访时间: 2018年12月13日)
- 报告: Dimension of invariant measures for affine iterated function systems (2018年12月13日，下午 15:00--16:00， 闵行数学楼401室)
- 摘要：In mathematics, iterated function system is one of the main schemes in generating fractal sets and measures. In this talk,
I will report some recent advances in dimension theory of stationary measures for affine iterated function systems.
Jiang Kan (蒋侃) ： 宁波大学数学系
(来访时间: 2018年11月21日至11月23日)
- 报告: Arithmetic on self-similar sets (2018年11月22日，下午 15:00--16:00， 闵行数学楼401室)
Dongkui Ma (马东魁) ： 华南理工大学数学科学学院
(来访时间: 2018年10月29日至10月30日)
- 报告: Topological entropy of free semigroup actions for noncompact sets (2018年10月29日，下午13:00--14:00，闵行数学楼102室)
- 摘要： In this paper we introduce the topological entropy and lower and upper capacity topological entropies of a free semigroup action, which extends the notion of the topological entropy of a
free semigroup action defined by Bufetov, by using the Caratheodory-Pesin structure (C-P structure). We provide some properties of these notions and give three main results. The first is the
relationship between the upper capacity topological entropy of a skew-product transformation and the upper capacity topological entropy of a free semigroup action with respect to arbitrary subset.
The second are a lower and a upper estimations of the topological entropy of a free semigroup action by local entropies. The third is that for any free semigroup action with m generators of Lipschitz maps,
topological entropy for any subset is upper bounded by the Hausdorff dimension of the subset multiplied by the maximum logarithm of the Lipschitz constants. The results of this paper generalize
results of Bufetov, Ma et al. , and Misiurewicz .
(来访时间: 2018年10月15日至10月23日)
- 报告: Numbers with simply normal β-expansions
(2018年10月22日，下午:13：00--14:00，闵行数学楼102室)
- 摘要：When β ∈ (1,2) it is well-known that almost every x ∈ [0, 1/(β-1)] has a continuum of β-expansions. In this talk we show that there exists a critical base
β_T ≈ 1.80194, the unique zero in (1,2) of the polynomial x^3-x^2-2x+1, such that for β ∈ (1, β_T] every interior point of [0, 1/(β-1)] has a simply normal β-expansion,
while for β ∈ (β_T, 2) there exists a point in [0, 1/(β-1)] that does not have a simply normal β-expansion. This is a joint work with Simon Baker.
(来访时间: 2018年10月9日至10月10日)
- 报告: BASES WITH TWO EXPANSIONS (2018年10月10日，上午9:00--10:00，闵行数学楼402室)
- 摘要： Given a dynamical system, we say that a performance function has property P if its time averages along orbits are maximized at a periodic orbit. It is
conjectured by several authors that for sufficiently hyperbolic dynamical systems, property P should be typical among sufficiently regular performance functions.
In this talk， we address this problem using a probabilistic notion of typicality that is suitable to infinite dimension: the concept of prevalence as introduced by Hunt,
Sauer, and Yorke. For the one-sided shift on two symbols, we prove that property P is prevalent in spaces of functions with a strong modulus of regularity. Our proof uses
Haar wavelets to approximate the ergodic optimization problem by a finite-dimensional one, which can be conveniently restated as a maximum cycle mean problem on a
de Bruijin graph. If time permits, I will also discuss the applications of the above combinatorial optimization methods in dealing with (non)-Sturiman maximizing (open)
problems for doubling maps.
The context of this talk has been presented as the first part of my collaborator Prof. Jairo Bochi’s 45 minutes short talk at ICM in Rio de Janeiro, 2018.
(来访时间: 2018年9月30日)
- 报告: Kaehler hyperbolic manifolds and Chern number inequalities (2018年9月29日，下午14:00--15:00，闵行数学楼401室)
- 摘要: In this talk we will review two well-known conjectures due to Hopf and S.-T. Yau respectively, and explain their connections via the concept of ``Kaehler hyperbolicity" introduced by Gromov.
Then we shall report our recent work around Kaehler hyperbolic manifolds.
(来访时间: 2017年11月3日至11月23日)
- 报告: BASES WITH TWO EXPANSIONS (2017年11月17日，上午10:10--11:10，闵行数学楼401室)
(来访时间: 2017年11月16日至11月19日)
- 报告: Covering lemma and univoque sets (2017年11月17日，上午 9:00--10:00， 闵行数学楼401室)
(来访时间: 2017年11月8日至11月10日)
- 报告: The sum-free set correspongding to Cantor-like sequence (2017年11月9日，上午10:10--11:10，闵行数学楼401室)
(来访时间: 2017年11月8日至11月10日)
- 报告: 临界点集与临界值集的分形结构
(2017年11月9日，上午9:00--10:00，闵行数学楼401室)
(来访时间: 2016年12月21日至12月25日)
- 报告: Porosities of fractal percolation (2016年12月22日下午15:00--16:00)
IN SOO BAEK：韩国Pusan University of Foreign Studies教授
(来访时间:2016/7/11－2016/7/24)
(来访时间: 2016年4月9日至4月12日)
- 报告: 有限自动机与代换生成的序列及相关研究问题 (2016年4月11日下午13:00--14:00)
(来访时间: 2016年4月6日至4月7日)
- 报告: 自相似集的一些近期进展和问题 ( 2016年4月7日上午10:00--11:00)
(来访时间: 2016年3月27日至4月10日)
- 报告一: Approximation properties of beta-expansions (2016年3月28日下午13:00--14:00)
- 报告二: Induced random beta transformations (2016年4月5日下午15:00--16:00)
Karma Dajani ：荷兰 Utrecht University 数学系
(来访时间: 2016年3月22日至30日)
- 报告: An excursion with Beta-expansions (2016年3月23日下午13:00--14:00)
Cornelis Kraaikamp ：荷兰Delft University of Technology数学系
(来访时间: 2016年3月22日至30日)
- 报告: Continued fractions and Diophantine approximation
(2016年3月23日下午14:15--15:15)
(来访时间: 2016年3月21日至30日)
- 报告: Multiple codings for self-similar sets with overlaps
(2016年3月28日下午14:15--15:15)
(来访时间: 2016年3月21日)
- 报告: On the rational approximation of automatic real numbers
(2016年3月21日下午13:00--14:00)
(来访时间: 2016年3月7日至8日)
- 报告: On the mixing properties of piecewise expanding maps under composition with permutations
(2016年3月7日下午13:00--14:00)
Jun Kigami
： 日本东京大学数学系教授
(来访时间: 2015年11月15日至21日)
- 报告: Analysis on fractals
(2015年11月17日下午13:00--14:30)
Sara Munday
： 英国York university数学系
(来访时间: 2015年9月12日至26日)
- 报告一: Topological Conjugacy maps ---- Minkowski's question-mark function and generalizatios （Lecture 1）
(2015年9月18日下午14:30--16:00)
- 报告二: Topological Conjugacy maps ---- Minkowski's question-mark function and generalizatios （Lecture 2）
(2015年9月21日下午13:00--14:30)
Sascha Troscheit
： 英国University of St Andrews数学系
(来访时间: 2015年6月30日至7月20日)
- 报告: Dimensions of random graph directed attractors
(2015年7月2日下午13:00--14:00)
(来访时间: 2015年3月17日至24日)
- 报告: Expansions in non-integer bases
(2015年3月19日下午13:00--14:00)
IN SOO BAEK：韩国Pusan University of Foreign Studies教授
(来访时间:2014/7/3－2014/7/25)
Jon Fraser：英国University of St Andrews数学系
(来访时间: 2012/12/3－2012/12/9)
- 报告: Generic dimensions of graphs and images
(2012年12月7日下午13:00--14:00)
IN SOO BAEK：韩国Pusan University of Foreign Studies教授
(来访时间: 2012/9/6－2013/3/6)
(来访时间: 2012年8月10日至24日)
- 报告: From Farey and Gauss to modern dynamical number theory
(2012年8月12日下午13:00--14:00)
Lars Olsen : 英国University of St Andrews教授
(来访时间:2011/7/14-2011/7/29)
- 报告一:Multifractals, Baire category and shyness
- 报告二:Multifractal tube formulas and multifractal zeta functions
- 报告三:Distribution of digits in integers
- 报告四:Normal and non-normal points of self-similar sets and divergence points of self-similar measures
IN SOO BAEK：韩国Pusan University of Foreign Studies教授
(来访时间:2010/8/9-2010/8/30)
- 报告一: The singularity order of the singular function
- 报告二: Multifractal analysis and applications
(来访时间:2010/8/22-2010/9/6)
- 报告一: Symmetry and Enumeration of Self-similar Fractals
- 报告二: Distance set
- 报告三: Self-affine sets and Measures
- 报告四: Visibility of fractals
范爱华：法国Picardie大学教授
(来访时间:2010/7/10-2010/7/13)
- 报告： Covering numbers of different points in Dvoretzky covering
(来访时间:2010/3/７-2010/3/13)
- 报告一: Geometric measure theory in Heisenberg groups (I).
- 报告二: Geometric measure theory in Heisenberg groups (II)
文志英： 清华大学数学系教授
(来访时间: 2009年12月6日至10日)
- 报告: Self-similarity of Satisfiable Boolean Expressions (2009年12月7日下午15:00--16:00)
Jeff Geronimo ：美国佐治亚理工大学数学系（School of Mathematics， Georgia Institute of Technology）教授
(来访时间:2009/6/21-2009/6/26)
- 报告：Fractal Interpolation Functions and the construction of compactly supported continuous, orthogonal wavelets: A dynamical systems approach (2009年6月22日下午16:00--17:00)
(来访时间:2007/10/28-2007/10/31)
- 报告一: Rectifiability in Geometric Measure Theory.
- 报告二: Rectifiability, singular integrals and removable sets.
- 报告三: Rectifiability in Geometric Measure Theory.
(来访时间:2004/10/3-2004/10/30)
- 报告一: On the size of the algebraic difference of two random Cantor sets
- 报告二: Random fractals