The morphology of MSS-sequences in a wide class of unimodal maps, its structure and decomposition

Abstract

The MSS-sequences (U-sequences) in a wide class of unimodal maps have the look $\mathrm{P}=(\mathrm{R}{\mathrm{L}}^q{)}^{n_1}{\mathrm{S}}_1(m_1,q-1)(\mathrm{R}{\mathrm{L}}^q{)}^{n_2}{\mathrm{S}}_2(m_2,q-1)$ $\dots$ $(\mathrm{R}{\mathrm{L}}^q{)}^{n_r}$ ${\mathrm{S}}_r(m_r,q-1)\mathrm{C},$ 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 first block ${\mathrm{RL}}^q$ and the sequence ${\mathrm{S}}_1$ following it are essential for an admissible sequence to be a MSS-sequence. Moreover ${\mathrm{S}}_i(m_i,q-1),i=2,\dots ,r$ are determined by ${\mathrm{S}}_1(m_1,q-1)$. Explicit structure of MSS-sequences will be given as well as the theorems that decompose the non-primary MSS-sequences. The cardinality will be calculated for some important sets of non-primary MSS-sequences and an algorithm to generate the blocks ${\mathrm{S}}_i(m_i,q-1),i=1,\dots ,r$ will be provided, as the construction of the blocks ${\mathrm{S}}_i(m_i,q-1)$ allows the construction of the MSS-sequences.

References in corpus (1)

• Continuous symmetry reduction and return maps for high-dimensional flows