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Historic behavior in nonhyperbolic homoclinic classes


Authors: Pablo G. Barrientos, Shin Kiriki, Yushi Nakano, Artem Raibekas and Teruhiko Soma
Journal: Proc. Amer. Math. Soc. 148 (2020), 1195-1206
MSC (2010): Primary 37C05, 37C20, 37C25, 37C29, 37C70
DOI: https://doi.org/10.1090/proc/14809
Published electronically: October 28, 2019
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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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Additional Information

Pablo G. Barrientos
Affiliation: Institute of Mathematics and Statistics, University Federal Fluminense-UFF, Gragoata Campus, Rua Prof. Marcos Waldemar de Freitas Reis, S/n-Sao Domingos, Niteroi - Rio de Janeiro, 24210-201, Brazil
Email: pgbarrientos@id.uff.br

Shin Kiriki
Affiliation: Department of Mathematics, Tokai University, 4-1-1 Kitakaname, Hiratuka, Kanagawa, 259-1292, Japan
Email: kiriki@tokai-u.jp

Yushi Nakano
Affiliation: Department of Mathematics, Tokai University, 4-1-1 Kitakaname, Hiratuka, Kanagawa, 259-1292, Japan
Email: yushi.nakano@tsc.u-tokai.ac.jp

Artem Raibekas
Affiliation: Institute of Mathematics and Statistics, University Federal Fluminense-UFF, Gragoata Campus, Rua Prof. Marcos Waldemar de Freitas Reis, S/n-Sao Domingos, Niteroi - Rio de Janeiro, 24210-201, Brazil
Email: artem@mat.uff.br

Teruhiko Soma
Affiliation: Department of Mathematical Sciences, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo 192-0397, Japan
Email: tsoma@tmu.ac.jp

DOI: https://doi.org/10.1090/proc/14809
Received by editor(s): May 12, 2019
Received by editor(s) in revised form: July 22, 2019
Published electronically: October 28, 2019
Additional Notes: The first author was supported by the project MTM2017-87697-P from Ministerio de Economía y Competividad de España and funded by CNPQ-Brasil.
This work was partially supported by JSPS KAKENHI Grants Nos. 17K05283, 18K03376
Dedicated: Dedicated to Hiroshi Kokubu for his $60$th birthday
Communicated by: Wenxian Shen
Article copyright: © Copyright 2019 American Mathematical Society