We face the problem of characterizing the periodic cases in parametric families of rational diffeomorphisms of k, where is R or C, having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two- and three-dimensional classes of polynomial or rational maps. In particular, we find the global periodic cases for several Lyness-type recurrences. © 2013 World Scientific Publishing Company.
|Journal||International Journal of Bifurcation and Chaos in Applied Sciences and Engineering|
|Publication status||Published - 1 Jan 2013|
- Globally periodic recurrences
- Lyness-type recurrences
- Normal forms
- Periodic maps
- Rational parametrizations