Let be a compact and connected smooth manifold endowed with a smooth action of a finite group , and let be a -invariant Morse function on . We prove that the space of -invariant Riemannian metrics on contains a residual subset with the following property. Let and let be the gradient vector field of with respect to . For any diffeomorphism preserving there exists some and some such that for every we have , where is the time- flow of the vector field .
Cite this article
Ignasi Mundet i Riera, Automorphisms of generic gradient vector fields with prescribed finite symmetries. Rev. Mat. Iberoam. 35 (2019), no. 5, pp. 1281–1308DOI 10.4171/RMI/1083