边界碰撞分岔序列对应的锁相阶梯

摘要

In a system described by a discontinuous map often a sequence of periodic orbits appears before chaotic motion. Transfer between the adjacent orbits happens via a border-collision bifurcation. The quantity, which symbolizes each orbit, usually is locked onto a lot of rational numbers to form a staircase. The staircase usually shows a form of conventional devil's staircase in one-dimensional maps and a form of complicated multiple devil's staircase in two or even higher dimensional dissipative maps. The complexity of the structure of the staircase depends on the number of the collision modes that the system can display. Similar staircases may be observed in discontinuous conservative maps but with very different properties.