Riv. Mat. Univ. Parma, Vol. 11, No. 1, 2020

Giuseppe Della Sala [a]

Prolongation of diffeomorphisms and smoothness of invariant submanifolds

Pages: 99-122
Received: 14 January 2019
Accepted: 25 June 2019
Mathematics Subject Classification (2010): 37F99, 32V40.
Keywords: Local diffeomorphism, invariant submanifolds, smoothness and analyticity.
Authors address:
[a]: Department of Mathematics, American University of Beirut, Riad El Sohl, Beirut, Lebanon

Abstract: We study various questions related to the smoothness of a real submanifold $$M$$ which is invariant under a family of real-analytic or holomorphic diffeomorphisms. We show that in various situations it is possible to conclude that $$M$$ is necessarily real-analytic (or the same smoothness of the diffeomorphisms involved if these are not analytic). The prolongation method we use also allows to recover some known results by employing relatively simple tools.

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