The general framework of Poincarè＇s formalism is used to establish the connection between conservation laws and invariance properties of Hamilton＇s function under infinitesimal transformations when these laws a...The general framework of Poincarè＇s formalism is used to establish the connection between conservation laws and invariance properties of Hamilton＇s function under infinitesimal transformations when these laws and the Hamiltonian are time-dependent. An example illustrative of the theory is also considered.展开更多
In this paper we show the distribution of critical points at infinity of n- dimensional polynomial differential systems, and give the conditions, under which the system is degenerate at infinity. Also, we discuss the...In this paper we show the distribution of critical points at infinity of n- dimensional polynomial differential systems, and give the conditions, under which the system is degenerate at infinity. Also, we discuss the quadratic systems with degenerate infinity, and obtain some similar properties to 2-dimensional quadratic systems.展开更多
文摘The general framework of Poincarè＇s formalism is used to establish the connection between conservation laws and invariance properties of Hamilton＇s function under infinitesimal transformations when these laws and the Hamiltonian are time-dependent. An example illustrative of the theory is also considered.
文摘In this paper we show the distribution of critical points at infinity of n- dimensional polynomial differential systems, and give the conditions, under which the system is degenerate at infinity. Also, we discuss the quadratic systems with degenerate infinity, and obtain some similar properties to 2-dimensional quadratic systems.
