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原文連結
論文資訊
- 類型：已發表論文
- 日期：2024-12-13
摘要
The Gauss map (or continued fraction map) is an important dissipative one-dimensional discrete-time dynamical system that exhibits chaotic behavior, and it generates a symbolic dynamics consisting of infinitely many different symbols. Here we introduce a generalization of the Gauss map, which is given by xt+1 = 1 where alpha 0 is a parameter and xt is an element of [0, 1] (t = 0, 1, 2, 3, ...). The symbol [... ] denotes the integer part. This map reduces to the ordinary Gauss map for alpha = 1. The system exhibits a sudden "jump into 混沌" at the critical parameter value alpha = alpha c equivalent to 0.241485141808811 ... which we analyze in detail in this paper. Several analytical and numerical results are established for this new map as a function of the parameter alpha. In particular, we
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