Abstract
The celebrated Brouwer translation theorem asserts that for a preserving orientation fixed point free homeomorphism of the plane, each point belongs to an invariant region where the dynamics is continuously conjugate to a translation. In this work we prove that if we start with a \({\mathcal {C}}^m, m\in {\mathbb {N}}\cup \{\infty \},\) diffeomorphism then the referred conjugacy has the same kind of regularity.
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Acknowledgements
The first author is partially supported by the project PID2019-104658GB-I00 grant) and Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R &D (CEX2020-001084-M), and the third author by the project MTM2017-86795-C3-1-P, all of the Spanish Ministerio de Ciencia e Innovación. The first and third authors are also supported by the grant 2017-SGR-1617 from AGAUR, Generalitat de Catalunya. The second author is partially supported by CSIC group 618-Uruguay.
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Gasull, A., Groisman, J. & Mañosas, F. Regularization of Brouwer Translation Theorem. Qual. Theory Dyn. Syst. 21, 135 (2022). https://doi.org/10.1007/s12346-022-00666-y
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DOI: https://doi.org/10.1007/s12346-022-00666-y