Rational dynamical zeta functions for birational transformations
We propose a conjecture for the exact expression of the unweighted dynamical zeta function for a family of birational transformations of two variables, depending on two parameters. This conjectured function is a simple rational expression with integer coefficients. This yields an algebraic value for the topological entropy. Furthermore, the generating function for the Arnold complexity is also conjectured to be a rational expression with integer coefficients with the same singularities as for the dynamical zeta function. This leads, at least in this example, to an equality between the Arnold complexity and the exponential of the topological entropy. We also give a semi-numerical method to effectively compute the Arnold complexity.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 264 (1999)
Issue (Month): 1 ()
|Contact details of provider:|| Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Boukraa, S. & Maillard, J-M. & Rollet, G., 1994. "Integrable mappings and polynomial growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 209(1), pages 162-222.
- Boukraa, S & Maillard, J-M, 1995. "Factorization properties of birational mappings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 220(3), pages 403-470.
- Boukraa, S. & Hassani, S. & Maillard, J.-M., 1997. "New integrable cases of a Cremona transformation: a finite-order orbits analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 240(3), pages 586-621.
When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:264:y:1999:i:1:p:264-293. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.