TY - JOUR
T1 - C0-Gap Between Entropy-Zero Hamiltonians and Autonomous Diffeomorphisms of Surfaces
AU - Brandenbursky, Michael
AU - Khanevsky, Michael
N1 - Funding Information:
We thank the referee for suggestions regarding the organization of the text. M. B. was partially supported by a Humboldt research fellowship.
Publisher Copyright:
© 2022, The Hebrew University of Jerusalem.
PY - 2022/12/5
Y1 - 2022/12/5
N2 - Let Σ be a surface equipped with an area form. There is a long-standing open question by Katok, which, in particular, asks whether every entropy-zero Hamiltonian diffeomorphism of a surface lies in the C0-closure of the set of integrable diffeomorphisms. A slightly weaker version of this question asks: “Does every entropy-zero Hamiltonian diffeomorphism of a surface lie in the C0-closure of the set of autonomous diffeomorphisms?”
AB - Let Σ be a surface equipped with an area form. There is a long-standing open question by Katok, which, in particular, asks whether every entropy-zero Hamiltonian diffeomorphism of a surface lies in the C0-closure of the set of integrable diffeomorphisms. A slightly weaker version of this question asks: “Does every entropy-zero Hamiltonian diffeomorphism of a surface lie in the C0-closure of the set of autonomous diffeomorphisms?”
UR - http://www.scopus.com/inward/record.url?scp=85143654439&partnerID=8YFLogxK
U2 - 10.1007/s11856-022-2418-z
DO - 10.1007/s11856-022-2418-z
M3 - Article
SN - 0021-2172
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
ER -