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An algorithm for counting the number of periodic points of a family of polynomials | ||
| Journal of Discrete Mathematics and Its Applications | ||
| دوره 9، شماره 4، اسفند 2024، صفحه 249-267 اصل مقاله (366.13 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2024.11165.1084 | ||
| نویسندگان | ||
| Monireh Akbari* 1؛ Maryam Rabii2 | ||
| 1Department of Mathematics, Faculty of Basic Sciences, Shahid Rajaee Teacher Training University, Tehran, Iran | ||
| 2Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University,Tehran, Iran | ||
| تاریخ دریافت: 03 آبان 1403، تاریخ بازنگری: 15 آبان 1403، تاریخ پذیرش: 29 آبان 1403 | ||
| چکیده | ||
| In this paper we consider the family fa(x) = axd(x − 1) + x when a < 0 is a real number and d ≥ 2 is an even integer. The function fa has a unique positive critical point. By decreasing the parameter a, the behavior of the orbit of this critical point changes. In this paper we consider two cases. In the first case the orbit of the positive critical point converges to 0 and in the second case the positive critical point is mapped to a repelling periodic point of period 2. In each case we give a recursive formula to determine the number of the periodic points of fa. Also, in each case we introduce an invariant set on which fa is chaotic. We employ conjugacy map and symbolic dynamics in our investigations. | ||
| کلیدواژه‌ها | ||
| Cantor set؛ chaos؛ conjugacy؛ periodic points؛ symbolic dynamics | ||
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آمار تعداد مشاهده مقاله: 10 تعداد دریافت فایل اصل مقاله: 10 |
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