Middle-dimensional squeezing and non-squeezing phenomena in Hamiltonian dynamics on finite dimensional and infinite-dimensional phase spaces

有限维和无限维相空间哈密顿动力学中的中维挤压和非挤压现象

• 批准号: 242354134
• 负责人: Professor Dr. Alberto Abbondandolo
• 金额: --
• 依托单位: Lehrstuhl Analysis (Prof. Abbondandolo)
• 依托单位国家: 德国
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/242354134?language=en
• 关键词: Middle; dimensional; squeezing; non; phenomena

Symplectomorphisms are the natural transformations of Hamiltonian dynamics. The celebrated non-squeezing theorem of Gromov states that no symplectomorphism can map the ball of radius r into the cylinder of radius s

辛同构是哈密顿动力学的自然变换。著名的Gromov非压缩定理指出，没有一个辛同胚可以把半径为r的球映射到半径为s的圆柱上

项目成果

A non-squeezing theorem for convex symplectic images of the Hilbert ball

希尔伯特球凸辛像的非挤压定理

• DOI: 10.1007/s00526-015-0832-3
• 发表时间: 2015
• 期刊: Calculus of Variations and Partial Differential Equations
• 影响因子: 2.1
• 作者: A. Abbondandolo;P. Majer
• 通讯作者: P. Majer

Chain Recurrence, Chain Transitivity, Lyapunov Functions and Rigidity of Lagrangian Submanifolds of Optical Hypersurfaces

• DOI: 10.1007/s10884-016-9543-5
• 发表时间: 2018-03-01
• 期刊: JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
• 影响因子: 1.3
• 作者: Abbondandolo, Alberto;Bernardi, Olga;Cardin, Franco
• 通讯作者: Cardin, Franco

A systolic inequality for geodesic flows on the two-sphere

二球体上测地线流动的收缩不等式

• DOI: 10.1007/s00208-016-1385-2
• 发表时间: 2017
• 期刊: Mathematische Annalen
• 影响因子: 1.4
• 作者: A. Abbondandolo;B. Bramham;U. Hryniewicz;P. Salomão
• 通讯作者: P. Salomão