ON A GENERALIZATION OF THE MORSE INDEX

摘要: Publisher Summary This chapter describes an index for the isolated invariant sets of a flow on compact metric space that, in case elementary singular points above, contains (exactly) information Morse index. is defined terms special isolating neighborhoods called blocks. A point ordinary differential equation if eigenvalues linearized equations all have non-zero real parts. In this case, set orbits that tends to has dimension equal number with negative part; unstable manifold complementary dimension. Either these dimensions determines near up conjugacy; thus, their importance not overemphasized by giving them name. It customary call point. Elementary are examples sense they admit closed neighborhood which maximal. Any such will be set. The definition implies any larger quite bit larger.