Abstract: The finite global attractor problem for polynomial case was recently solved by using tree lifting algorithm. Since the global contraction rate of the simplicial map of the tree complex is in general unclear, it is not known how fast the pull backs of a curve converge to the attractors.  In the work we will introduce the ideas of quick returns and barrier lakes to analyze the combinatorial models of curves. These allow us to prove that the complexity of a curve is exponentially decreased under the pull backs by the iteration of a polynomial. 

Zoom Meeting ID: 181 155 584