Abstract
Jones and Boston conjectured that the factorization process for iterates of irreducible quadratic polynomials over finite fields is approximated by a one-step Markov model. In this paper, we find unexpected and intricate behavior for some quadratic polynomials, in particular for those whose critical orbits have large cycle and small tail. We also propose a multistep Markov model that explains these new observations better than the model of Jones and Boston. © 2014 Taylor and Francis Group, LLC.
| Original language | English |
|---|---|
| Pages (from-to) | 304-311 |
| Journal | Experimental Mathematics |
| Volume | 24 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 3 Jul 2015 |
| Externally published | Yes |
Bibliographical note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].Research Keywords
- factorization
- Iteration
- Markov process
- quadratic polynomial
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