Historic behavior in nonhyperbolic homoclinic classes

Barrientos, Pablo; Kiriki, Shin; Nakano, Yushi; Raibekas, Artem; Soma, Teruhiko

doi:10.1090/proc/14809

Historic behavior in nonhyperbolic homoclinic classes
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by Pablo G. Barrientos, Shin Kiriki, Yushi Nakano, Artem Raibekas and Teruhiko Soma PDF

Proc. Amer. Math. Soc. 148 (2020), 1195-1206 Request permission

Abstract:

We show that $C^1$-generically for diffeomorphisms of manifolds of dimension $d\geq 3$, a homoclinic class containing saddles of different indices has a residual subset where the orbit of any point has historic behavior.

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