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2013
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# Boris Petković

KTH Royal Institute of Technology

## Publications:

 Petković B. Classification of Perturbations of Diophantine $\mathbb{Z}^m$ Actions on Tori of Arbitrary Dimension 2021, vol. 26, no. 6, pp.  700-716 Abstract We generalize results of Moser [17] on the circle to $\mathbb{T}^d$: we show that a smooth sufficiently small perturbation of a $\mathbb Z^m$ action, $m \geqslant 2$, on the torus $\mathbb{T}^d$ by simultaneously Diophantine translations, is smoothly conjugate to the unperturbed action under a natural condition on the rotation sets of diffeomorphisms isotopic to identity and we answer the question Moser posed in [17] by proving the existence of a continuum of $m$-tuples of simultaneously Diophantine vectors such that every element of the induced $\mathbb Z^m$ action is Liouville. Keywords: KAM theory, simultaneously Diophantine translations, local rigidity, simultaneously Diophantine approximations Citation: Petković B.,  Classification of Perturbations of Diophantine $\mathbb{Z}^m$ Actions on Tori of Arbitrary Dimension, Regular and Chaotic Dynamics, 2021, vol. 26, no. 6, pp. 700-716 DOI:10.1134/S1560354721060083