Francesco Calogeroのセミナー（４月１４日）のご案内 (English at the Bottom)： ローマ大学（ラ・サピエンザ）物理学科のFrancesco Calogero教授が，日本学 術振興会招へい外国人学者（短期）として１ヶ月半京都大学基礎物理学研究所 に滞在しています．Calogero氏は，多体問題，ソリトン理論，可解系の著名な 研究者で，今回は多体可解系の最近の話題について，基礎物理学研究所談話会 で話をします． 日時：２００６年４月１４日（金）１３：３０〜１４：３０ 場所：京都大学基礎物理学研究所，研究棟２階K202 講師：Francesco Calogero　ローマ大学（ラ・サピエンザ） 演題：Isochronous systems are not rare 梗概：A dynamical system is called isochronous if it features an open (hence fully dimensional) region in its phase space in which all its solutions are completely periodic (i. e., periodic in all degrees of freedom) with the same fixed period (independent of the initial data, provided they are inside the isochronicity region). A trick is presented associating to a dynamical system a modified system depending on a real parameter so that when this parameter vanishes the original system is reproduced while when this parameter does not vanish the modified system is isochronous. This technique is applicable to large classes of dynamical systems, justifying the title of this talk. An analogous technique, even more widely applicable - for instance, to any translation-invariant (classical) many-body problem ? transforms a Hamiltonian system to an isochronous Hamiltonian system. This last finding is joint work with Francois Leyvraz. Francesco Calogero氏は基礎物理学研究所に４月１６日まで滞在し，次の週は 東京近郊でいくつかのセミナーをしますので，その日時，演題・梗概について もお知らせします． 日時：２００６年４月１８日（火）15:00〜16:00 場所：高エネルギー加速器研究機構　素粒子原子核研究所理論部 演題：A direct technique to identify solvable dynamical systems, and some solvable extensions of the goldfish many-body problem 日時：２００６年４月１９日（水）16:00〜 場所：東京工業大学大岡山キャンパス本館１階 H1-36 演題：The transition from regular to irregular motions, explained as travel on Riemann surfaces 日時：２００６年４月２０日（木）１３：３０〜 場所：東京大学理学部物理４号館３階１３２０号室 演題：A direct technique to identify solvable dynamical systems, and some solvable extensions of the goldfish many-body problem 日時：２００６年４月２１日（金）１４：００〜 場所：東京理科大学理工学部（野田キャンパス）４号館３階数学科セミナー室 演題：Isochronous systems are not rare セミナーの梗概 演題：A direct technique to identify solvable dynamical systems, and some solvable extensions of the goldfish many-body problem 梗概：A (somewhat novel) technique to identify and investigate solvable many-body problems is described, and it is shown that it reproduces some standard many-body problems already known to be integrable and solvable, as well as some new ones. Some of these new models are isochronous, namely their generic solutions are completely periodic with a fixed period (independent of the initial data). The investigation of the behavior of some of these systems in the vicinity of their equilibrium configurations yields some amusing diophantine relations. 演題：The transition from regular to irregular motions, explained as travel on Riemann surfaces 梗概：We introduce and discuss a simple Hamiltonian dynamical system, interpretable as a 3-body problem in the (complex) plane and providing the prototype of a mechanism explaining the transition from regular to irregular motions as travel on Riemann surfaces. The interest of this phenomenology -- illustrating a mechanism for the onset in a deterministic context of irregular motions -- is underlined by its generality, suggesting its eventual relevance to understand natural phenomena and experimental investigations. This is joint work with David Gomez-Ullate, Paolo Santini and Matteo Sommacal. 文責：京都大学基礎物理学研究所　佐々木隆 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Seminars by Francesco Calogero (14 April): Professor Francesco Calogero (Department of Physics, University of Rome, La Sapienza) is now visiting Yukawa Institute for Theoretical Physics, Kyoto University, funded by Japan Society of Promotion of Science, Invitation Fellowship Program (Short Term) for 1 and 1/2 months. He is a renowned researcher of Many-body problem, Soliton theory and Integrable systems. He delivers a talk on his recent work in many-body integrable systems. Date:14 April 2006 (Friday) 13:30-14:30 Place: Yukawa Insiutute for Theoretical Physics, Kyoto University, Main Building2nd Floor K202 Title:Isochronous systems are not rare Abstract:A dynamical system is called isochronous if it features an open (hence fully dimensional) region in its phase space in which all its solutions are completely periodic (i. e., periodic in all degrees of freedom) with the same fixed period (independent of the initial data, provided they are inside the isochronicity region). A trick is presented associating to a dynamical system a modified system depending on a real parameter so that when this parameter vanishes the original system is reproduced while when this parameter does not vanish the modified system is isochronous. This technique is applicable to large classes of dynamical systems, justifying the title of this talk. An analogous technique, even more widely applicable - for instance, to any translation-invariant (classical) many-body problem ? transforms a Hamiltonian system to an isochronous Hamiltonian system. This last finding is joint work with Francois Leyvraz. Francesco Calogero will stay at YTukawa Institute till 16 April and he will deliver several seminars in Tokyo region in the following week. Date: 18 April 2006 (Tuesday) 15:00--16:00 Place: High Energy Accelerator Research Organization, Institute of Particle and Nuclear Studies, Theory Group Title: A direct technique to identify solvable dynamical systems, and some solvable extensions of the goldfish many-body problem Date: 19 April 2006 (Wednesday) 16:00-- Place: Tokyo Insitute of Technology, O-okayama Campus Main Building, Ground Floor H1-36 Title:The transition from regular to irregular motions, explained as travel on Riemann surfaces Date: 20 April 2006 (Thursday) 13:30-- Place: University of Tokyo, Physics Department, science building 4, 3rd Floor, room 1320 Title:A direct technique to identify solvable dynamical systems, and some solvable extensions of the goldfish many-body problem Date: 21 April 2006 (Friday) 14:00-- Place: Science University of Tokyo, Faculty of Science and Technology (Noda Campus), Building 4, 3rd Floor, Mathematics Seminar Room Title: Isochronous systems are not rare Here are the Abstracts of two other Talks: Title: A direct technique to identify solvable dynamical systems, and some solvable extensions of the goldfish many-body problem Abstract: A (somewhat novel) technique to identify and investigate solvable many-body problems is described, and it is shown that it reproduces some standard many-body problems already known to be integrable and solvable, as well as some new ones. Some of these new models are isochronous, namely their generic solutions are completely periodic with a fixed period (independent of the initial data). The investigation of the behavior of some of these systems in the vicinity of their equilibrium configurations yields some amusing diophantine relations. Title: The transition from regular to irregular motions, explained as travel on Riemann surfaces Abstract: ：We introduce and discuss a simple Hamiltonian dynamical system, interpretable as a 3-body problem in the (complex) plane and providing the prototype of a mechanism explaining the transition from regular to irregular motions as travel on Riemann surfaces. The interest of this phenomenology -- illustrating a mechanism for the onset in a deterministic context of irregular motions -- is underlined by its generality, suggesting its eventual relevance to understand natural phenomena and experimental investigations. This is joint work with David Gomez-Ullate, Paolo Santini and Matteo Sommacal. Ryu SASAKI, Yukawa Institute for Theoretical Physics, Kyoto University