Open Access
2014 Dynamics of (pseudo) automorphisms of 3-space: periodicity versus positive entropy
Eric Bedford, Kyounghee Kim
Publ. Mat. 58(1): 65-119 (2014).


We study the iteration of the family of maps given by $3$-step linear fractional recurrences. This family was studied earlier from the point of view of finding periodicities. In this paper we finish that study by determining all possible periods within this family. The novelty of our approach is that we apply the methods of complex dynamical systems. This leads to two classes of interesting pseudo automorphisms of infinite order. One of the classes consists of completely integrable maps. The other class consists of maps of positive entropy which have an invariant family of $K3$ surfaces.


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Eric Bedford. Kyounghee Kim. "Dynamics of (pseudo) automorphisms of 3-space: periodicity versus positive entropy." Publ. Mat. 58 (1) 65 - 119, 2014.


Published: 2014
First available in Project Euclid: 20 December 2013

zbMATH: 1295.37014
MathSciNet: MR3161509

Primary: 14E07 , 32F10 , 32H50 , 32M99

Keywords: $K3$ surfaces , birational map , dynamical degree , periodicity , Pseudo-automorphism , rational $3$ fold , rational recurrences

Rights: Copyright © 2014 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.58 • No. 1 • 2014
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