Integrability of Hamiltonian system with homogeneous polynomial potential of degree four

Suman Babu

The analysis of non-linear dynamical problems is important in both mathematical and physical point of view. The non-linear systems are not explicitly solvable and they are chaotic depending upon the value of the control parameters. From physical point of view, the existence of integrable nonlinear dynamical systems often means the existence of very regular motion. From mathematical point of view, they imply the existence of beautiful analytic and geometric structures. The concept of integrability is itself in a sense not well defined and seems to be no unique definition. The integrability nature of dynamical systems can be methodologically investigated using the following two broad notions (1) Integrability in the complex time plane: Painleve Property (2) Complete Integrability and Liouville Integrability. In this paper the Painleve method is used to check the integrability of Hamiltonian system. The main objective of this work is to analyses the integrability of Hamiltonian system with a homogeneous polynomial potential of degree four using Painleve test.