Estimation Of The Upper Bound Of The Number Of Limit Cycles For Three Types Of Planar Piecewise Linear Hamiltonian Systems Under Two Different Perturbation

The chang-4 probe was successfully launched in the early morning of December 8.2018.And on January 3,2019.it,as successfully landed on the lunar south pole.During the period.The chang-4 probe was required to undergo launching orbiting,orbit the Earth,transfer from the Earth to the moon.fly around the moon,and finally land on the moon.The resistance and gravity of each process are different.In order to minimize the fuel consumption,researchers can approximate the entire launching process as a piecewise smooth ordilary differential equation.which can lbe calculatod to optimize the control strategy.Therefore,piecewise smooth ordinary differential equations have a wide range of applications in real life.So it is very important to study piecewise smooth ordinary dinereiitial cequations.In this paper.the author considers the near Bogdanov-Takens system as the right subsystem,and considers the parabolic near-Hamilton system or the elliptical noar-Hnulilton system or the hyperbola near-Hamilton system as the left subsystem.When the perturbation is Lienard perturbation P+(x,y)= P-(x,y)=0 or polynomial perturbationand the author calculate the upper bound of the number of limit cycles,witch the above piecewise smooth near-Hamilton svstem bifurcates.In the first chapter.the author introduces the development history of ordinary differential equations.makes a brief sumlary of the research status of the piecewise smooth Hamilton system.and introduces the main findings of this paper.The second chapter is preparatory knowledge,including several lemmas and propositions related to this article.In the third chapter,the author studies the first order Melnikov function of under two different perturbation of right Bogdanov-Takens subsystem,and the left Parabolic Hamilton subsystem.elliptical Hamilton subsystem,hyperbola Hamilton subsystem.In the fourth chapter,the author proves the main results theorem 1.theorem 2 and theorem 3 of this paper.