学术报告

罗马第一大学F. Calogero教授系列学术报告 [2009-05-07]

报告题目:Isochronous systems

报 告 人:F. Calogero教授

报告时间:11月3日(周一),下午4:10―5:10

报告地点:理化中心大楼16008

主办单位:数学系,数学所

欢迎感兴趣的师生参加!!!

F. Calogero 简介: 罗马第一大学物理系教授、国际知名的数学物理专家,在量子场论,多体问题,散射理论,可积系统等方面均有杰出工作,发表学术论文总计300多篇,专著3本,包括建立非等谱问题的反散射方法,提出了量子多体问题中非常有名的可解模型:Calogero-Sutherland 模型等等.在学术上有广泛国际交往和影响, 是多个国际会议的学术组织人和多个刊物、丛书编委。从1989-1997,他担任Pugwash Conferences on Science and World Affair的秘书长,并于1995年10月代表该组织接受Nobel 和平奖。他另外还有非学术的论文400篇。 他定期来科大访问,在中国科大与罗马大学的学术交流中起了积极促进作用。

本次访问安排(10.31-11.11):近年来,他在同步系统研究中取得了很多成果,在牛津大学出版专著一部:Isochronous systems(Oxford University Press,2008.)。本此次来访,将安排3次报告系统介绍他的最新工作,例如化学反应中的震荡和同步系统。

摘要: A vector-valued time-dependent function is called isochronous if all its components are periodic in time with the same fixed period T. A dynamical system is called isochronous if its generic solution is isochronous: periodic in all its degrees of freedom with a fixed period T independent of the initial data (in its entire phase space, or possibly in an---open, fully-dimensional---subregion of it). It will be shown how essentially any (autonomous) dynamical system can be modified into another (autonomous) dynamical systems which is isochronous with an (arbitrarily !) assigned period T, and which moreover behaves, over time periods very short with respect to T, essentially as the original (unmodified) system---up to a constant time rescaling. This can also be done for dynamical systems which are Hamiltonian (both the unmodified and the modified one), including that describing the most general many-body problem. Some implications of this fact for statistical mechanics and thermodynamics will be discussed, related to the tricky question of the irreversibility of macroscopic phenomena. The more general possibility will also be discussed to generate systems which are asymptotically isochronous, whose generic (vector-valued) solutions tend to isochronous (vector-valued) functions in the remote future.

The main focus of this series of lectures will be on (systems of) nonlinear ordinary differential equations, but if time permits analogous results for partial differential equations will also be mentioned.

The material that will be covered includes that reported in my recent monograph (Isochronous systems, Oxford University Press, 2008), as well as very recent findings obtained together with F. Leyvraz.


报告题目:Isochronous systems

报 告 人:F. Calogero教授

报告时间:11月5日(周三),下午4:10―5:10

报告地点:理化中心大楼16008

主办单位:数学系,数学所

欢迎感兴趣的师生参加!!!

F. Calogero 简介: 罗马第一大学物理系教授、国际知名的数学物理专家,在量子场论,多体问题,散射理论,可积系统等方面均有杰出工作,发表学术论文总计300多篇,专著3本,包括建立非等谱问题的反散射方法,提出了量子多体问题中非常有名的可解模型:Calogero-Sutherland 模型等等.在学术上有广泛国际交往和影响, 是多个国际会议的学术组织人和多个刊物、丛书编委。从1989-1997,他担任Pugwash Conferences on Science and World Affair的秘书长,并于1995年10月代表该组织接受Nobel 和平奖。他另外还有非学术的论文400篇。 他定期来科大访问,在中国科大与罗马大学的学术交流中起了积极促进作用。

本次访问安排(10.31-11.11):近年来,他在同步系统研究中取得了很多成果,在牛津大学出版专著一部:Isochronous systems(Oxford University Press,2008.)。本此次来访,将安排3次报告系统介绍他的最新工作,例如化学反应中的震荡和同步系统。

摘要: A vector-valued time-dependent function is called isochronous if all its components are periodic in time with the same fixed period T. A dynamical system is called isochronous if its generic solution is isochronous: periodic in all its degrees of freedom with a fixed period T independent of the initial data (in its entire phase space, or possibly in an---open, fully-dimensional---subregion of it). It will be shown how essentially any (autonomous) dynamical system can be modified into another (autonomous) dynamical systems which is isochronous with an (arbitrarily !) assigned period T, and which moreover behaves, over time periods very short with respect to T, essentially as the original (unmodified) system---up to a constant time rescaling. This can also be done for dynamical systems which are Hamiltonian (both the unmodified and the modified one), including that describing the most general many-body problem. Some implications of this fact for statistical mechanics and thermodynamics will be discussed, related to the tricky question of the irreversibility of macroscopic phenomena. The more general possibility will also be discussed to generate systems which are asymptotically isochronous, whose generic (vector-valued) solutions tend to isochronous (vector-valued) functions in the remote future.

The main focus of this series of lectures will be on (systems of) nonlinear ordinary differential equations, but if time permits analogous results for partial differential equations will also be mentioned.

The material that will be covered includes that reported in my recent monograph (Isochronous systems, Oxford University Press, 2008), as well as very recent findings obtained together with F. Leyvraz.


报告题目:Isochronous systems

报 告 人:F. Calogero教授

报告时间:11月7日(周五),下午4:10―5:10

报告地点:理化中心大楼16008

主办单位:数学系,数学所

欢迎感兴趣的师生参加!!!

F. Calogero 简介: 罗马第一大学物理系教授、国际知名的数学物理专家,在量子场论,多体问题,散射理论,可积系统等方面均有杰出工作,发表学术论文总计300多篇,专著3本,包括建立非等谱问题的反散射方法,提出了量子多体问题中非常有名的可解模型:Calogero-Sutherland 模型等等.在学术上有广泛国际交往和影响, 是多个国际会议的学术组织人和多个刊物、丛书编委。从1989-1997,他担任Pugwash Conferences on Science and World Affair的秘书长,并于1995年10月代表该组织接受Nobel 和平奖。他另外还有非学术的论文400篇。 他定期来科大访问,在中国科大与罗马大学的学术交流中起了积极促进作用。

本次访问安排(10.31-11.11):近年来,他在同步系统研究中取得了很多成果,在牛津大学出版专著一部:Isochronous systems(Oxford University Press,2008.)。本此次来访,将安排3次报告系统介绍他的最新工作,例如化学反应中的震荡和同步系统。

摘要: A vector-valued time-dependent function is called isochronous if all its components are periodic in time with the same fixed period T. A dynamical system is called isochronous if its generic solution is isochronous: periodic in all its degrees of freedom with a fixed period T independent of the initial data (in its entire phase space, or possibly in an---open, fully-dimensional---subregion of it). It will be shown how essentially any (autonomous) dynamical system can be modified into another (autonomous) dynamical systems which is isochronous with an (arbitrarily !) assigned period T, and which moreover behaves, over time periods very short with respect to T, essentially as the original (unmodified) system---up to a constant time rescaling. This can also be done for dynamical systems which are Hamiltonian (both the unmodified and the modified one), including that describing the most general many-body problem. Some implications of this fact for statistical mechanics and thermodynamics will be discussed, related to the tricky question of the irreversibility of macroscopic phenomena. The more general possibility will also be discussed to generate systems which are asymptotically isochronous, whose generic (vector-valued) solutions tend to isochronous (vector-valued) functions in the remote future.

The main focus of this series of lectures will be on (systems of) nonlinear ordinary differential equations, but if time permits analogous results for partial differential equations will also be mentioned.

The material that will be covered includes that reported in my recent monograph (Isochronous systems, Oxford University Press, 2008), as well as very recent findings obtained together with F. Leyvraz.