Diffeomorphisms of the torus with wandering domains

McSwiggen, Patrick D.

doi:10.1090/S0002-9939-1993-1154247-6

Diffeomorphisms of the torus with wandering domains
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by Patrick D. McSwiggen

Proc. Amer. Math. Soc. 117 (1993), 1175-1186

DOI: https://doi.org/10.1090/S0002-9939-1993-1154247-6

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Abstract:

Examples of ${C^{3 - \varepsilon }}$ diffeomorphisms of the $2$-torus are constructed, each of which is semiconjugate to an ergodic translation but has a wandering domain with dense orbit. This is a generalization of a classical example on the circle due to Denjoy.

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