第一年, 預計將研讀 entropy 和 dimension 進一步論文, 更深入研究具有 非自治動力系統的軌跡函數之entropy 架構. 例如, 在機率空間和緊緻距 離拓樸群空間, 兩者都有不同的entropy 定義和結構, 計劃探究尋找彼此 性質和關係. 也計劃擴展measure-theoretic entropy 定義至topological pre-image pressure,尋找變數法則. 第二年, 預估非自治動力系統之條件 熵將有上半連續(upper semicontinuity)的性質, 共同擁有遍歷架構, 亦 期望發現 Birkhoff Ergodic Theorem 相似成果. 第三年, 最後, 計劃要把 碎形與條件熵具體的結果應用在電腦裏, 例如壓縮、放大電腦圖片. During this project, I plan to research forward iterated non-autonomous dynamical systems, including some ergodic properties of commuting functions and the sub-additivity properties of fractal geometry on the invariant set. At first, two papers“Topological entropy of non-autonomous dynamical systems＂and“Positive entropy on non-autonomous interval maps and the topology of the inverse limit space＂will be studied and try to obtain the relationship between conditional entropy and Hausdorff dimension.
