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首页> 外文期刊>Discrete and continuous dynamical systems▼hSeries S >STABLE SETS OF PLANAR HOMEOMORPHISMS WITH TRANSLATION PSEUDO-ARCS
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STABLE SETS OF PLANAR HOMEOMORPHISMS WITH TRANSLATION PSEUDO-ARCS

机译：具有翻译伪弧的稳定的平面常态套

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摘要

For every n∈ N we construct orientation preserving planar home- omorphisms gn such that Fix(g_n) = {0}, the fixed point index of g_n at 0, i_(R~2) (g_n, 0), is equal to-n and the stable (respectively unstable) sets of g_n at 0 decompose into exactly n + 1 connected branches {S_j}_(j∈{1,2,...,n+1}) (resp. {U_j}_(j∈{1,2,...,n+1g)) such that: a) S_i ∩ S_j = {0} = U_i ∩ U_j for any i,j∈ {1, 2,... n + 1} with i≠j. b) S_i ∩ U_j = {0} for any i, j∈ {1,2,... n + 1}. c) For every j∈ {1, 2,...n + 1}, S_j{0} and U_j{0} admit translation pseudo-arcs. This means that there exist pseudo-arcs K_j⊂ S_j and points p_(j*), g_n(p_(j*))∈ K_j,such that gn(K_j) ∩ K_j = {g_n(p_(j*))} and S_j{0} =∞∪m=-∞g~m_n(K_j) and analogously for Uj . We also study the closure of the class of above homeomorphisms in the (complete) metric space of planar orientation preserving homeomorphisms.
机译：对于每个N∈N，我们构建方向保留平面家庭 - amorphisms gn，使得fix（g_n）= {0}，g_n处的固定点索引为0，i_（r〜2）（g_n，0）等于 - n和0at的稳定（分别不稳定）设置为0分解成恰好n + 1连接的分支{s_j} _（j∈{1,2，...，n + 1}）（resp。{u_j} _（ J∈{1,2，...，n + 1g））这样：a）s_i∩s_j = {0} = u_i∩u_jfor任何i，j∈{1,2，... n + 1}用i∈J。 b）对于任何i，j∈{1,2，... n + 1}，s_i∩u_j= {0}。 c）对于每个J∈{1,2，... n + 1}，s_j {0}和u_j {0}承认翻译伪弧。这意味着存在伪弧k_j⊂s_j和点p_（j *），g_n（p_（j *））∈k_j，使得gn（k_j）∩k_j= {g_n（p_（j *））}} s_j {0} =∞∪m=-əg〜m_n（k_j），类似于UJ。我们还研究了平面定向保存同源术的（完整）公制空间中的上述同源术等级。

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