This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invarianee being Lie symmetrical simultaneously by the...This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invarianee being Lie symmetrical simultaneously by the action of infinitesimal transformations are given. The determining equations of the conformal invariance are gained. Then the Hojman conserved quantities of conformal invariance by special infinitesimal transformations are obtained. Finally an illustrative example is given to verify the results.展开更多
The chaotification problem of discrete Hamilton systems in one dimensional space is investigated and corresponding chaotification theorem is established. Feedback control techniques is used to make arbitrary discrete ...The chaotification problem of discrete Hamilton systems in one dimensional space is investigated and corresponding chaotification theorem is established. Feedback control techniques is used to make arbitrary discrete Hamilton systems chaotic, or enhance its existing chaotic behaviors. By designing a universal controller and combining anti-integrable limit it is proved that chaos of the controlled systems is in the sense of Devaney. In particular, the systems corresponding to the original systems and designed controllers are only required to satisfy some mild assumptions. Moreover, the range of the coefficient of the controller is given.展开更多
A new method is introduced in this paper. This method can be used to study the stability of controlled holonomic Hamilton systems under disturbance of Gaussian white noise. At first, the motion equation of controlled ...A new method is introduced in this paper. This method can be used to study the stability of controlled holonomic Hamilton systems under disturbance of Gaussian white noise. At first, the motion equation of controlled holonomic Hamilton systems excited by Gaussian noise is formulated. A theory to stabilize the system is provided. Finally, one example is given to illustrate the application procedures.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos 10472040,10572021 and 10772025)the Outstanding Young Talents Training Found of Liaoning Province of China (Grant No 3040005)
文摘This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invarianee being Lie symmetrical simultaneously by the action of infinitesimal transformations are given. The determining equations of the conformal invariance are gained. Then the Hojman conserved quantities of conformal invariance by special infinitesimal transformations are obtained. Finally an illustrative example is given to verify the results.
基金the National Natural Science Foundation of China(10272022)
文摘The chaotification problem of discrete Hamilton systems in one dimensional space is investigated and corresponding chaotification theorem is established. Feedback control techniques is used to make arbitrary discrete Hamilton systems chaotic, or enhance its existing chaotic behaviors. By designing a universal controller and combining anti-integrable limit it is proved that chaos of the controlled systems is in the sense of Devaney. In particular, the systems corresponding to the original systems and designed controllers are only required to satisfy some mild assumptions. Moreover, the range of the coefficient of the controller is given.
基金Sponsored by the National Natural Science Foundation of China (1057202110472040)Fundamental Research Foundation of Beijing Institute of Technology (BIT-UBF-200507A4206)
文摘A new method is introduced in this paper. This method can be used to study the stability of controlled holonomic Hamilton systems under disturbance of Gaussian white noise. At first, the motion equation of controlled holonomic Hamilton systems excited by Gaussian noise is formulated. A theory to stabilize the system is provided. Finally, one example is given to illustrate the application procedures.
