Explosions in completely unstable flows. I. Preventing explosions

Zbigniew Nitecki
1978 Transactions of the American Mathematical Society  
Several conditions are equivalent to the property that a now (on an open manifold) and its C° perturbations have only wandering points. These conditions are: (i) there exists a strong Liapunov function; (ii) there are no generalized recurrent points in the sense of Auslander; (iii) there are no chain recurrent points, in the sense of Conley; (iv) there exists a fine sequence of nitrations; (v) relative to some metric; the flow is the gradient flow of a function without critical points. We
more » ... ish these equivalences, and consider a few questions related to structural stability when all orbits wander.
doi:10.1090/s0002-9947-1978-0511399-2 fatcat:5q5szivfzfaf3pv43kqiamvuwe