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The morphology of allowed sequences in unimodal maps, its structure and decomposition. (arXiv:1706.07676v1 [math.DS])

来源于:arXiv
The allowed sequences in a discrete unimodal system look like $\mathrm{P}=(\mathrm{R} \mathrm{L}^{q})^{n_1} \mathrm{S}_1(m_1,q-1) (\mathrm{R} \mathrm{L}^{q})^{n_2}\mathrm{S}_2(m_2,q-1) $ $\ldots$ $ (\mathrm{R} \mathrm{L}^{q})^{n_r} \mathrm{S}_r(m_r,q-1)\mathrm{C}$ where $\mathrm{S}_i(m_i, q-1)$ are sequences of $\mathrm{R}$s and $\mathrm{L}$s that contain at most $q-1$ consecutive $\mathrm{L}$s. The $\mathrm{S}_i(m_i,q-1), \ i=2, \ldots, r$ are determined by $\mathrm{S}_1(m_1,q-1)$. The first block $\mathrm{RL}^q$ and the sequence $\mathrm{S}_1$ following it are essential for a sequence to be allowed. In addition $\mathrm{RL}^q$ and $\mathrm{S}_1$ also govern the composition of sequences, since every non-primary sequence has the form $\mathrm{RL}^q \mathrm{S}_1(m_1,q-1)\mathrm{C} \ast \mathrm{x_1,\ldots x_{s-1}C}.$ Explicit forms of allowed sequences will be given. Also their cardinality will be calculated. 查看全文>>