In the present report, we analyze the behavior of the bifurcated points appearing through anomalous rotation bifurcation in the two dimensional map defined below. T_m : y_n+1 = y_n + a(x_n − x_n^m), x_n+1 = x_n + y_n+1 (a ≥ 0, m ≥ 2). Let a_c(p/q) be the critical value at which the rotation bifurcation of the elliptic fixed point Q occurs, a_c^sn(p/q) be the critical value at which the saddle-node bifurcation happens and a_c^isn(p/q) be the critical value at which the inverse saddle-node bifurcation happens. Here p/q is the rotation number of the bifurcated periodic orbit. First, we explain the well known anomalous rotation bifurcation named type I. The saddle and elliptic points appear at a = a_c^sn(p/q)(< a_c(p/q)). After the saddle-node bifurcation, the saddle point gradually approaches the elliptic fixed point (Q) and the saddle point collides with Q at a_c(p/q). Next, we explain two anomalous rotation bifurcations named type II-A and type II-B found in this paper. Suppose that the saddle-node bifurcation occurs after the rotation bifurcation of Q. The saddle point appeared through the saddle-node bifurcation collides with the elliptic point appeared through the rotation bifurcation at a = a_c^isn(p/q)(> a_c^sn(p/q) > a_c(p/q)). This is named type II-A. Suppose that the rotation bifurcation of Q occurs after the saddle-node bifurcation occurs. The saddle point appeared through the saddle-node bifurcation collides with the elliptic point appeared through the rotation bifurcation at a = a_c^isn(p/q)(> a_c(p/q) > a_c^sn(p/q)). This is named type II-B. The bifurcation processes of types I, II-A and II-B are studied and these differences are discussed.

This paper develops an analytical model for analyzing the effect of the floor shape on the travel distances outside and inside a building. The average distances outside and inside a building are obtained for a multi-story building with rectangular floors in a rectangular site. The analytical expressions for the average distances show how the floor shape and the location of entrances affect the distances. The average distance outside the building increases (decreases) with the aspect ratio of floors in a square (rectangular) site. The average distance inside the building increases with the aspect ratio. The entrances at the four corners of the building can decrease the distance outside the building but increase the distance inside the building.