Dynamics in two complex dimensions
John Smillie
我们描述的结果的动态多项式的同构的${\bf C^2}$和绘制连接的动态多项式映射的${\bf C}$和动态的多项式同构的${\bf R^2}$，如Hénon家庭。
We describe results on the dynamics of polynomial diffeomorphisms of ${\bf C^2}$ and draw connections with the dynamics of polynomial maps of ${\bf C}$ and the dynamics of polynomial diffeomorphisms of ${\bf R^2}$ such as the Hénon family.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Density of Orbits in Complex Dynamics
本文讨论了Cerveau提出的关于复动力学中轨道密度的一个问题
This is an expository plus research paper which mainly exposes preliminary connection and contrast between classical complex dynamics and semigroup dynamics of holomorphic functions. Classically, we expose some existing results of rational and transcendental dynamics and we see how far these results generalized to holomorphic semigroup dynamics as well as we also see what new phenomena occur.
Transformations, Dynamics and Complexity
我们回顾和研究了由映射迭代、β-变换、划分、群作用、丛动力系统、Hasse-Kloosterman映射和系统复杂性的某些方面所产生的动力系统领域的一些新问题和结果。
The dynamics of the classical Lorenz system is well studied in $1963$ by E. N. Lorenz. Later on, there have been an extensive studies on the classical Lorenz system with the complex variables and the discrete time Lorenz system with real variables. To the best of knowledge of the author, so far there is no study on discrete time Lorenz system in complex variables. In this article, an attempt has been made to observe and understand the discrete dynamics of the Lorenz system with complex variables. This study compares the discrete dynamics of the Lorenz system with complex variables to that of t…
These are notes from elementary lectures given in the summer of 2013 at the YMSC center at Tsinghua University in Beijing.
Dynamics of quadratic polynomials: Complex bounds for real maps
我们扩展沙利文的复杂的先验界，真正的二次多项式与本质上有界组合。结合第一作者以前的结果，这产生了所有实二次函数的复界。相应的朱利亚集的局部连通性如下。
Dynamics of the delay rational difference equation $\displaystyle{z_{n+1}=\frac{α+βz_{n-k}}{γ- z_{n}}}$ with complex parameters $α$, $β$, $γ$ and arbitrary complex initial conditions is investigated. Existence of prime period two solutions and higher order periods are ensured in the complex parameters unlike in the case of real parameters of the same rational difference equation. In addition, a new dynamical behavior, chaotic solutions of the difference equation are ensured computationally.
There are many research papers dealing with fractal dimension of real-valued fractal functions in the recent literature. The main focus of the present paper is to study fractal dimension of complex-valued functions. This paper also highlights the difference between dimensional results of the complex-valued and real-valued fractal functions. In this paper, we study the fractal dimension of the graph of complex-valued function $g(x)+i h(x)$, compare its fractal dimension with the graphs of functions $g(x)+h(x)$ and $(g(x),h(x))$ and also obtain some bounds. Moreover, we study the fractal dimensi…
We provide a generalization of the McMullen's algorithm to approximate the Hausdorff dimension of the limit set for convex-cocompact subgroups of isometries of the Complex Hyperbolic Plane.
Dimensionality Reduction in Stochastic Complex Dynamical Networks
针对现有降维方法多假设系统为确定性、难以适配真实随机系统的问题，本文提出一种随机复杂动态网络降维通用分析框架，可将高维随机系统映射为低维等效系统，还能借助等效方程标准差分析网络的动力学行为与收敛性。
We survey some of the connections linking complex dynamics to other fields of mathematics and science. We hope to show that complex dynamics is not just interesting on its own but also has value as an applicable theory.
Fekete sequences in complex dynamics
本文已被arXiv：1106.3367取代
Lyapunov exponents in complex dynamics and potential theory
本文由arXiv：1106.3363取代。
Complex dimension of additive subgroups of R^{n}
本文定义了R^{n}$的任意可加子群的复维数，推广了向量空间的欧氏维数.我们给出了一个明确的方法来计算这个尺寸。
Complex dynamics in several variables
这些笔记是一系列讲座的产物在MSRI在1995年1月在开始的特殊学期在复杂的动力学和双曲几何。在这些笔记中，主要目的是激发两个变量的复杂动力学的研究，并介绍该领域的主要思想。因此，对这个问题的处理大多是暂时的。
Complex dynamics and invariant forms mod p
黎曼球面上的复杂动力系统不具有“不变形式”。然而，存在定义在数域上的动力系统的非平凡的例子，满足它们的归约模$\wp$对于除了1000个地方之外的所有地方都具有“不变形式”的性质$\wp$。本文完全刻画了具有后一性质的动力系统。
Multifractal formalism for expanding rational semigroups and random complex dynamical systems
本文研究了黎曼球面上有理映射半群动力学和随机复动力系统的重分形形式。我们详细阐述了一个多重分形分析的水平集的Birkhoff和关于斜积与一个半群的合理的映射。应用这些结果，我们对随机复动力系统极限状态函数的Hölder正则性进行了多重分形分析。
Quantized vortex dynamics of the complex Ginzburg-Landau equation on torus
该研究严格推导了环面上复金兹堡-朗道方程在涡旋核尺寸趋于零时的量子涡旋约化动力学定律，揭示其由重整化能量驱动的梯度流与哈密顿流混合支配，并探讨了对应的首次积分与解析解。
Rigidity in Complex Dynamics: Multiplier Spectrum and Dynamical André-Oort Conjecture
本研究介绍一维复动力学刚性问题的近期进展，证明了曲线的动力André-Oort猜想及乘子谱的一般单射性，其证明结合代数几何、Arakelov几何与复动力学思想。
Complex dynamics with focus on the real parts
我们考虑$\mathbb C$中全纯多项式的动力学。我们证明了该映射的遍历性质已经可以从轨道的实部看出。
We give a formula to compute the dimension of the generic component of the moduli space of an irreducible germ of curve in the complex plane.
On the Dynamics of Complex Quadratic Families under Holomorphic and Non-Holomorphic Singular Perturbations
本文研究复二次映射在全纯和非全纯奇异扰动下的动力学特性，探讨其拓扑和统计性质。
Dynamics of automorphisms on projective complex manifolds
我们证明了所有射影复流形X（3维，或任何维，但假设良好的极小模型程序或Mori's程序）上的自同构的动力学是从三种类型的射影复流形上的动力学正则地建立起来的：复环面、弱卡-丘流形和有理连通流形。作为副产品，我们证实了Guedj关于三维射影流形上自同构的猜想，并确定了pi_1（X）。
A new partition identity coming from complex dynamics
我们提出了一个新的身份涉及的组成（即有序分区的自然数）。该公式起源于复杂的动力系统，并出现在计算时，在多项式族$\{f_c:z \mapsto z^d + c \}$，周期临界轨道与等效行程。我们给出了两种不同的证明身份，一个是在动力学和另一个纯粹的组合方法的原始方法。
We consider the general model for dynamical systems defined on a simplicial complex. We describe the conjugacy classes of these systems and show how symmetries in a given simplicial complex manifest in the dynamics defined thereon, especially with regard to invariant subspaces in the dynamics.
Dynamics of Singular Holomorphic Foliations on the Complex Projective Plane
这份手稿是介绍复射影平面上的全纯叶理理论。从历史上看，这个问题已经出现在理论的常微分方程在复杂的领域和各种尝试解决希尔伯特的第16问题，但随着引进复杂的代数几何，叶理理论和动力系统，它现在已经成为一个有趣的主题。
We give an interpretation of the Riemann hypothesis in terms of complex and topological dynamics. For example, the Riemann hypothesis is affirmative and all zeros of the Riemann zeta function are simple if and only if a certain meromorphic function has no attracting fixed point. To obtain this, we use holomorphic index (residue fixed point index), which characterizes local properties of fixed points in complex dynamics.
On the complex dynamics of birational surface maps defined over number fields
证明了复射影曲面的动力学度大于1且定义在数域上的任何双有理自映射在适当的双有理共轭后自动满足Bedford-Diller能量条件.因此，地图的复杂动力学表现良好。我们还表明，有一个定义良好的正则高度函数。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。