天元讲堂：（5.10）Transfer Operator, Gibbs measures and Equilibrium States
报告题目： Transfer Operator, Gibbs measures and Equilibrium States (part 1)
报告人 Renaud Leplaideur（新喀里多尼亚大学）
报告时间 2018年5月10日09:30-10:30
报告地点 维格堂119
报告摘要 Transfer Operator is a classical and very powerful tool to construct Gibbs measure for hyperbolic Dynamical Systems. It has been introduced in Dynamical Systems by Ruelle in the 70's. The lectures are mainly inspired from Bowen (LNM 470) and also Broise (Astérisque 1996, no. 238, 1–109.). We introduce some fundamental notations.
报告题目： Transfer Operator, Gibbs measures and Equilibrium States (part 2)
报告人 Renaud Leplaideur（新喀里多尼亚大学）
报告时间 2018年5月10日10:30-11:30
报告地点 维格堂119
报告摘要 In a first step, one will explain why Gibbs measures are Equilibrium States and give the explicit construction of Gibbs measures for subshift of finite type using the Transfer Operator.
报告题目： Transfer Operator, Gibbs measures and Equilibrium States (part 3)
报告人 Renaud Leplaideur（新喀里多尼亚大学）
报告时间 2018年5月10日11:30-12:30
报告地点 维格堂119
报告摘要 This lecture will show how the spectral properties of the Transfer Operator are related to ergodic properties of the system.
报告题目： Transfer Operator, Gibbs measures and Equilibrium States (part 6)
报告人 Renaud Leplaideur（新喀里多尼亚大学）
报告时间 2018年5月17日11:30-12:30
报告地点 维格堂119
报告摘要 One shall show how this theorem can be used to reformulate what Bowen did in its book for more general functional spaces. The proof of the ITM theorem will be given.
报告人 Renaud Leplaideur（新喀里多尼亚大学）
报告时间 2018年5月10日09:30-10:30
报告地点 维格堂119
报告摘要 Transfer Operator is a classical and very powerful tool to construct Gibbs measure for hyperbolic Dynamical Systems. It has been introduced in Dynamical Systems by Ruelle in the 70's. The lectures are mainly inspired from Bowen (LNM 470) and also Broise (Astérisque 1996, no. 238, 1–109.). We introduce some fundamental notations.
报告题目： Transfer Operator, Gibbs measures and Equilibrium States (part 2)
报告人 Renaud Leplaideur（新喀里多尼亚大学）
报告时间 2018年5月10日10:30-11:30
报告地点 维格堂119
报告摘要 In a first step, one will explain why Gibbs measures are Equilibrium States and give the explicit construction of Gibbs measures for subshift of finite type using the Transfer Operator.
报告题目： Transfer Operator, Gibbs measures and Equilibrium States (part 3)
报告人 Renaud Leplaideur（新喀里多尼亚大学）
报告时间 2018年5月10日11:30-12:30
报告地点 维格堂119
报告摘要 This lecture will show how the spectral properties of the Transfer Operator are related to ergodic properties of the system.
报告题目： Transfer Operator, Gibbs measures and Equilibrium States (part 4)
报告人 Renaud Leplaideur（新喀里多尼亚大学）
报告时间 2018年5月17日09:30-10:30
报告地点 维格堂119
报告摘要 The lecture will point out how the hyperbolic properties of the system and the regularity of the studied potential combine themselves to give nice spectral properties for the Transfer Operator.
报告题目： Transfer Operator, Gibbs measures and Equilibrium States (part 5)
报告人 Renaud Leplaideur（新喀里多尼亚大学）
报告时间 2018年5月17日10:30-11:30
报告地点 维格堂119
报告摘要 The lecture will mainly focus on some theorem for operators due to Ionescu-Tulcea and Marinescu in the 50's.
报告人 Renaud Leplaideur（新喀里多尼亚大学）
报告时间 2018年5月17日09:30-10:30
报告地点 维格堂119
报告摘要 The lecture will point out how the hyperbolic properties of the system and the regularity of the studied potential combine themselves to give nice spectral properties for the Transfer Operator.
报告题目： Transfer Operator, Gibbs measures and Equilibrium States (part 5)
报告人 Renaud Leplaideur（新喀里多尼亚大学）
报告时间 2018年5月17日10:30-11:30
报告地点 维格堂119
报告摘要 The lecture will mainly focus on some theorem for operators due to Ionescu-Tulcea and Marinescu in the 50's.
报告题目： Transfer Operator, Gibbs measures and Equilibrium States (part 6)
报告人 Renaud Leplaideur（新喀里多尼亚大学）
报告时间 2018年5月17日11:30-12:30
报告地点 维格堂119
报告摘要 One shall show how this theorem can be used to reformulate what Bowen did in its book for more general functional spaces. The proof of the ITM theorem will be given.