Topological Dynamics in Real and Complex Systems
真实和复杂系统中的拓扑动力学
基本信息
- 批准号:0140349
- 负责人:
- 金额:$ 8.42万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2002
- 资助国家:美国
- 起止时间:2002-08-01 至 2005-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The proposal deals with several topics in low-dimensionaldynamics. The PI plans to investigate the topological dynamicsof laminations; in particular he would like to further developthe dynamics of growing trees and use it to study the behaviorof the vertices of the Julia set. He also wants to consider classes of non-analytic plane maps for whom analogs of well-knownresults for polynomials can be proven. Other directions of hisresearch are related to attractos for classes of rational maps and to further developing the rotation theory which studies coexistence of cycles depending on their characteristics similarto rotation numbers for circle maps of degree one. The theory of dynamical systems gives tools to study complex systems, for example the evolution of a complicated deterministicprocess over time. There is a rich and distinguished tradition of using these powerful tools in other sciences like communication theory, statistical physics, and chemical kinetics.
该提案涉及低维动力学的几个主题。PI计划研究叠层的拓扑动力学;特别是他想进一步发展生长树的动力学,并用它来研究Julia集顶点的行为。他还想考虑类的非解析平面地图的人类似的众所周知的结果多项式可以证明。他的其他研究方向涉及吸引力类的合理地图和进一步发展的旋转理论,研究共存的周期取决于他们的特点类似旋转数的圆地图的程度之一。动力系统理论提供了研究复杂系统的工具,例如复杂的确定性过程随时间的演化。在通信理论、统计物理学和化学动力学等其他科学中使用这些强大的工具有着丰富而杰出的传统。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Alexander Blokh其他文献
Applications of almost one-to-one maps
- DOI:
10.1016/j.topol.2004.03.009 - 发表时间:
2006-04-01 - 期刊:
- 影响因子:
- 作者:
Alexander Blokh;Lex Oversteegen;E.D. Tymchatyn - 通讯作者:
E.D. Tymchatyn
Rotation Sets of Billiards with One Obstacle
- DOI:
10.1007/s00220-006-0014-4 - 发表时间:
2006-04-14 - 期刊:
- 影响因子:2.600
- 作者:
Alexander Blokh;Michał Misiurewicz;Nándor Simányi - 通讯作者:
Nándor Simányi
Attractors and recurrence for dendrite-critical polynomials
- DOI:
10.1016/j.jmaa.2004.10.038 - 发表时间:
2005-06-15 - 期刊:
- 影响因子:
- 作者:
Alexander Blokh;Michał Misiurewicz - 通讯作者:
Michał Misiurewicz
Rotational subsets of the circle under <math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll" class="math"><msup><mi>z</mi><mi>d</mi></msup></math>
- DOI:
10.1016/j.topol.2005.04.010 - 发表时间:
2006-04-01 - 期刊:
- 影响因子:
- 作者:
Alexander Blokh;James M. Malaugh;John C. Mayer;Lex G. Oversteegen;Daniel K. Parris - 通讯作者:
Daniel K. Parris
The Julia sets of quadratic Cremer polynomials
- DOI:
10.1016/j.topol.2006.02.001 - 发表时间:
2006-09-01 - 期刊:
- 影响因子:
- 作者:
Alexander Blokh;Lex Oversteegen - 通讯作者:
Lex Oversteegen
Alexander Blokh的其他文献
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{{ truncateString('Alexander Blokh', 18)}}的其他基金
Dynamical Systems and Ergodic Theory Conference
动力系统和遍历理论会议
- 批准号:
1501074 - 财政年份:2015
- 资助金额:
$ 8.42万 - 项目类别:
Standard Grant
Complex and real topological dynamics
复杂而真实的拓扑动力学
- 批准号:
1201450 - 财政年份:2012
- 资助金额:
$ 8.42万 - 项目类别:
Standard Grant
Laminations and Low-Dimensional Dynamical Systems
叠片和低维动力系统
- 批准号:
0456748 - 财政年份:2005
- 资助金额:
$ 8.42万 - 项目类别:
Standard Grant
Attractors, Smooth Dynamics and Combinatorics in Low-Dimension
低维吸引子、平滑动力学和组合学
- 批准号:
9970363 - 财政年份:1999
- 资助金额:
$ 8.42万 - 项目类别:
Standard Grant
Mathematical Sciences: Combinatorial and Measure-Theoretic Structure of Dynamical Systems
数学科学:动力系统的组合和测度理论结构
- 批准号:
9626303 - 财政年份:1996
- 资助金额:
$ 8.42万 - 项目类别:
Standard Grant
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