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

A NONINTEGRABILITY CRITERION FOR ADIABATIC SYSTEMS

2006 ◽  
Vol 16 (06) ◽  
pp. 1829-1833
Author(s):  
DESPINA VOYATZI ◽  
EFI MELETLIDOU
Keyword(s):  
Fixed Point ◽  
Time Dependence ◽  
Hamiltonian Systems ◽  
Additional Assumption ◽  
High Order ◽  
Degree Of Freedom ◽  
Unstable Fixed Point

In the present paper we investigate the nonintegrability of adiabatic one degree of freedom Hamiltonian systems, with the additional assumption that the frozen system possesses an unstable fixed point with two asymmetric homoclinic loops. We prove a criterion for the nonexistence of an integral for such systems, and therefore we prove the nonexistence of a quantity which is conserved in an arbitrarily high order on ε. A specific application is given in the asymmetric quartic oscillator with adiabatic time dependence.

High-Order Symplectic Schemes for Stochastic Hamiltonian Systems

2014 ◽  
Vol 16 (1) ◽  
pp. 169-200 ◽  
Author(s):  
Jian Deng ◽  
Cristina Anton ◽  
Yau Shu Wong
Keyword(s):  
Hamiltonian Systems ◽  
High Order ◽  
Symplectic Integrators ◽  
Symplectic Methods ◽  
Computational Tools ◽  
Fully Implicit ◽  
Stochastic Hamiltonian Systems ◽  
Hamiltonian Functions ◽  
Symplectic Schemes

AbstractThe construction of symplectic numerical schemes for stochastic Hamiltonian systems is studied. An approach based on generating functions method is proposed to generate the stochastic symplectic integration of any desired order. In general the proposed symplectic schemes are fully implicit, and they become computationally expensive for mean square orders greater than two. However, for stochastic Hamiltonian systems preserving Hamiltonian functions, the high-order symplectic methods have simpler forms than the explicit Taylor expansion schemes. A theoretical analysis of the convergence and numerical simulations are reported for several symplectic integrators. The numerical case studies confirm that the symplectic methods are efficient computational tools for long-term simulations.

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 On Passivity-Based High-Order Compensators for Mechanical Port-Hamiltonian Systems Without Velocity Measurements

2021 ◽  
Vol 54 (14) ◽  
pp. 287-292
Author(s):  
Kiyoshi Hamada ◽  
Pablo Borja ◽  
Kenji Fujimoto ◽  
Ichiro Maruta ◽  
Jacquelien M.A. Scherpen
Keyword(s):  
Hamiltonian Systems ◽  
High Order ◽  
Velocity Measurements
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