Laminations and Low-Dimensional Dynamical Systems
Laminations and Low-Dimensional Dynamical Systems
批准号:
0456748
负责人:
Alexander Blokh
金额:
$0.0万
依托单位国家:
美国
项目类别:
Standard Grant
财政年份:
2005
资助国家:
美国
项目状态:
已结题
起止时间:
2005-08-01 至 2008-07-31
中文摘要
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英文摘要
ABSTRACTThe proposal aims at developing new tools in low-dimensional dynamics. Studying laminations/polynomials requires a combination of techniques which already allowed us to show the existence of wandering gaps of laminations and should lead to the description of dynamics of an individual polynomial, and to the description of the combinatorial analog of the boundary of the connectedness locus (i.e., the Mandelbrot set for high degree polynomials). For the cycles of polynomials we plan to developthe rotation theory analogous to that for interval maps, and a version of the Sharkovskii theorem. We continue developing theory of c-tent plane maps which combine expansive properties of tent maps with properties of complex quadratic maps and should play the same role for quadratic complex maps as tent maps play on the interval. We also deal with Milnor attractors for conformal measures of complex maps, and work on some problems in interval dynamics.Some natural processes/maps are described by low-dimensional dynamical systems.The project aims at solving a few problems helping describe these maps,as well as their families. Among non-invertible maps in dimensions higherthan 1 the best in terms of their properties are complex polynomials, andwe plan to study the families of their combinatorial analogs for dimensions higher than 2, as well as individual polynomials in terms of the coexistenceof their cycles (periodic processes). We also study so-called c-tent map,Milnor attractors, and some problems for map of the interval.
期刊论文(0)
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会议论文
Dynamical Systems and Ergodic Theory Conference
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批准号:1501074
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项目类别:Standard Grant
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资助金额:$4.54万
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财政年份:2015
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负责人:Alexander Blokh
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依托单位:
Complex and real topological dynamics
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批准号:1201450
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项目类别:Standard Grant
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资助金额:$13.5万
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财政年份:2012
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负责人:Alexander Blokh
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依托单位:
Topology and Low-Dimensional Dynamics
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批准号:0901038
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项目类别:Standard Grant
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资助金额:$12.37万
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财政年份:2009
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负责人:Alexander Blokh
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依托单位:
Topological Dynamics in Real and Complex Systems
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批准号:0140349
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项目类别:Standard Grant
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资助金额:$8.42万
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财政年份:2002
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负责人:Alexander Blokh
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依托单位:
Attractors, Smooth Dynamics and Combinatorics in Low-Dimension
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批准号:9970363
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项目类别:Standard Grant
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资助金额:$7.13万
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财政年份:1999
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负责人:Alexander Blokh
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依托单位:
Mathematical Sciences: Combinatorial and Measure-Theoretic Structure of Dynamical Systems
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批准号:9626303
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项目类别:Standard Grant
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资助金额:$6.2万
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财政年份:1996
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负责人:Alexander Blokh
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依托单位:
国内基金
海外基金
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