scholarly journals Invariant Tori in Hamiltonian Systems with High Order Proper Degeneracy

2010 ◽  
Vol 10 (8) ◽  
pp. 1419-1436 ◽  
Author(s):  
Yuecai Han ◽  
Yong Li ◽  
Yingfei Yi
Keyword(s):  
Hamiltonian Systems ◽  
Invariant Tori ◽  
High Order

scholarly journals Arbitrary High-order EQUIP Methods for Stochastic Canonical Hamiltonian Systems

2019 ◽  
Vol 23 (3) ◽  
pp. 703-725 ◽  
Author(s):  
Xiuyan Li ◽  
Chiping Zhang ◽  
Qiang Ma ◽  
Xiaohua Ding
Keyword(s):  
Hamiltonian Systems ◽  
High Order

On the number of caustics for invariant tori of Hamiltonian systems with two degrees of freedom

1991 ◽  
Vol 11 (2) ◽  
pp. 273-278 ◽  
Author(s):  
Misha Bialy
Keyword(s):  
Hamiltonian Systems ◽  
Cotangent Bundle ◽  
Degrees Of Freedom ◽  
Invariant Tori ◽  
Hamiltonian Function ◽  
Canonical Projection ◽  
Classical Type ◽  
Two Dimensional ◽  
Hamiltonian Flow ◽  
Connected Manifold

Let X be a two-dimensional orientable connected manifold without boundary, H: T*X → ℝ a smooth hamiltonian function denned on the cotangent bundle. We will assume that H is of a ‘classical type’ that is convex and even on each fibre Tx*X. The goal of this paper is to describe the set Γ of all singular points of the projection Θ|L where ι: L → T*X is a smooth embedded 2-torus invariant under the hamiltonian flow h1, Θ: T*X → X is the canonical projection.

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