论文标题
正常形式，可区分的结合和地图的基本分叉
Normal forms, differentiable conjugacies and elementary bifurcations of maps
论文作者
论文摘要
我们加强了鞍形节点，跨念头，干草叉和周期倍增分叉的标准分叉定理。我们的新公式涉及在标准截短的正常形式中添加一个或两个额外的术语，并由代数方程确定的系数。这些扩展的正常形式与固定点或周期轨道的吸引力和排斥的盆地的原始地图有所不同。这反映了尽管仅根据拓扑等效性制定了标准分叉定理，但尽管标准分叉定理是正常形式中的其他信息的共同假设。
We strengthen the standard bifurcation theorems for saddle-node, transcritical, pitchfork, and period-doubling bifurcations of maps. Our new formulation involves adding one or two extra terms to the standard truncated normal forms with coefficients determined by algebraic equations. These extended normal forms are differentiably conjugate to the original maps on basins of attraction and repulsion of fixed points or periodic orbits. This reflects common assumptions about the additional information in normal forms despite standard bifurcation theorems being formulated only in terms of topological equivalence.
