# American Institute of Mathematical Sciences

March  2008, 1(1): 107-116. doi: 10.3934/dcdss.2008.1.107

## Arnold tongues for bifurcation from infinity

 1 Institute for Information Transmission Problems, Russian Academy of Sciences, 19 Bol.Karetny Lane, Moscow GSP-4, 127994, Russian Federation 2 Institute for Information Transmission Problems, Russian Academy of Sciences, 19 Bol.Karetny Lane, Moscow GSP-4, 127994, Russia; National Research University Higher School of Economics, 20 Myasnitskaya Street, Moscow 101000, Russian Federation 3 Department of Applied Mathematics, University College Cork, Cork, Ireland

Received  September 2006 Revised  January 2007 Published  December 2007

We consider discrete time systems $x_{k+1}=U(x_{k};\lambda)$, $x\in\R^{N}$, with a complex parameter $\lambda$. The map $U(\cdot;\lambda)$ at infinity contains a principal linear term, a bounded positively homogeneous nonlinearity, and a smaller part. We describe the sets of parameter values for which the large-amplitude $n$-periodic trajectories exist for a fixed $n$. In the related problems on small periodic orbits near zero, similarly defined parameter sets, known as Arnold tongues, are more narrow.
Citation: Victor S. Kozyakin, Alexander M. Krasnosel’skii, Dmitrii I. Rachinskii. Arnold tongues for bifurcation from infinity. Discrete and Continuous Dynamical Systems - S, 2008, 1 (1) : 107-116. doi: 10.3934/dcdss.2008.1.107
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