@article{f1f3d932b676494bbcff327af239b7ea,
title = "Anosov endomorphisms on the two-torus: regularity of foliations and rigidity",
abstract = "We provide sufficient conditions for smooth conjugacy between two Anosov endomorphisms on the two-torus. From that, we also explore how the regularity of the stable and unstable foliations implies smooth conjugacy inside a class of endomorphisms including, for instance, the ones with constant Jacobian. As a consequence, we have in this class a characterisation of smooth conjugacy between special Anosov endomorphisms (defined as those having only one unstable direction for each point) and their linearisations.",
keywords = "hyperbolic dynamics, non-invertible dynamics, smooth dynamics",
author = "Marisa Cantarino and R{\'e}gis Var{\~a}o",
note = "Funding Information: The authors would like to thank Boris Hasselblatt and Koichi Hiraide for kindly clarifying some points for section 2. We also thank the anonymous referees for the careful reading and valuable comments. M C was partially financed by the Coordena{\c c}{\~a}o de Aperfei{\c c}oamento de Pessoal de N{\'i}vel Superior—Brasil—Grant 88882.333632/2019-01 and the Funda{\c c}{\~a}o Carlos Chagas Filho de Amparo {\`a} Pesquisa of the State of Rio de Janeiro E-26/202.014/2022. R V was partially financed by CNPq and Fapesp Grants 18/13481-0 and 17/06463-3. Funding Information: The authors would like to thank Boris Hasselblatt and Koichi Hiraide for kindly clarifying some points for section . We also thank the anonymous referees for the careful reading and valuable comments. M C was partially financed by the Coordena{\c c}{\~a}o de Aperfei{\c c}oamento de Pessoal de N{\'i}vel Superior—Brasil—Grant 88882.333632/2019-01 and the Funda{\c c}{\~a}o Carlos Chagas Filho de Amparo {\`a} Pesquisa of the State of Rio de Janeiro E-26/202.014/2022. R V was partially financed by CNPq and Fapesp Grants 18/13481-0 and 17/06463-3. Funding Information: M C was partially financed by the Coordena{\c c}{\~a}o de Aperfei{\c c}oamento de Pessoal de N{\'i}vel Superior—Brasil—Grant 88882.333632/2019-01 and the Funda{\c c}{\~a}o Carlos Chagas Filho de Amparo {\`a} Pesquisa of the State of Rio de Janeiro E-26/202.014/2022. Funding Information: R V was partially financed by CNPq and Fapesp Grants 18/13481-0 and 17/06463-3. Publisher Copyright: {\textcopyright} 2023 IOP Publishing Ltd & London Mathematical Society.",
year = "2023",
month = oct,
day = "1",
doi = "10.1088/1361-6544/acf267",
language = "English",
volume = "36",
pages = "5334--5357",
journal = "Nonlinearity",
issn = "0951-7715",
publisher = "IOP Publishing",
number = "10",
}