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http://dspace.centre-univ-mila.dz/jspui/handle/123456789/3991| Title: | DISCRETE DYNAMICAL SYSTEM |
| Other Titles: | Course of Master 1 (first year) Fundamental and Applied Mathematics |
| Authors: | KHAOULA, ROUIBAH |
| Issue Date: | 3-Jun-2025 |
| Publisher: | University Center of Abdalhafid Boussouf - MILA |
| Description: | This comprehensive study reveals the mathematical structure of discrete-time dynamical systems, where simple recursive rules of the form xn+1 = f (xn) give rise to surprisingly rich and complex behaviors. Our exploration begins with the fundamental bridge between continuous and discrete systems (Section 1.1), where we develop the conceptual framework and precise terminology (Section 1.2) that underpin our entire investigation. Through careful analysis of system orbits (Section 1.3), we discover the ordered beauty of fixed points and periodic solutions (Section 1.4), while the powerful concept of topological equivalence (also in Section 1.4) reveals hidden connections between seemingly di erent systems. We illustrate this using vivid graphical methods (Section 1.6), where one-dimensional cobweb plots (Section 1.6.1) and two-dimensional phase portraits (Section 1.6.2) transform abstract concepts into visual intuition. |
| URI: | http://dspace.centre-univ-mila.dz/jspui/handle/123456789/3991 |
| Appears in Collections: | Mathematics |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| DISCRETE DYNAMICAL SYSTEM.pdf | 3,63 MB | Adobe PDF | View/Open |
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