# Math Events

## 《从守恒到耗散: 泛哈密顿系统的动力学与变分法》

### 第二周（2020-07-17，14:00-16:00）

Zoom会议: 690 776 66313 密码：123456

### 第三周（2020-07-24，14:00-16:00）

Zoom会议: 661 689 45483 密码：123456

### 第六周（2020-08-14，14:00-16:00）

#### Poincaré Mechanism in Multi-scaled Hamiltonian Systems

• At first, I will introduce the results in integrable Hamiltonian systems since what we focus on is nearly-integrable Hamiltonian system.
• The second part is the definition of nearly-integrable Hamiltonian system and the classical KAM theorem.
• After then, I will introduce that what is Poincaré problem and some interesting results corresponding to this problem.
• The last part, which is also the main part, I will talk about the definition and the back ground of nearly-integrable Hamiltonian system, then the persistence of lower dimensional tori on resonant surface, which is our recent result.

I will also simply introduce the Technical ingredients of our work.

### 第九周（2020-09-03，2020-09-04，15:00-16:00）

2020-09-03 Zoom: 646 976 07037 密码：123456

#### A price formation mean-field game model

2020-09-04 Zoom: 664 863 69095 密码：123456

### 第十一周（2020-09-14，11:00-12:00）

Zoom: 659 865 44977 密码：123456

### 第十二周（2020-09-25，14:00-15:00）

Zoom: 668 0410 3984 密码：123456

### 第十三周（2020-09-28，15:00-16:00）

Zoom: 650 0806 2145 密码：123456

### 第十七周（2020-10-30，14:00-16:00）

Zoom: 696 196 91647 密码：123456

### 第十八周（2020-11-02，15:30-16:30）

Zoom: 620 998 77902 密码：123456

### 第二十周（2020-11-16，16:00-17:00；2020-11-20，09：00-11：00）

2020-11-16，16:00-17:00 Zoom: 622 098 20563 密码：123456

#### Singularity Theory for non-twist tori

2020-11-20，09：00-11：00 Zoom: 687 466 26905 密码：123456

#### Whiskered KAM Tori of Conformally Symplectic Systems

Our main result is formulated in an a-posteriori format. Given an approximately invariant embedding of the torus for a parameter value $\mu_0$ with an approximately invariant splitting, there is an invariant embedding and invariant splittings for new parameters.

Using the results of formal expansions as the starting point for the a-posteriori method, we study the domains of analiticity of parameterizations of whiskered tori in perturbations of Hamiltonian Systems with dissipation. The proofs of the results lead to efficient algorithms that are quite practical to implement.

Joint work with A. Celletti and R. de la Llave, A.P. Bustamante.