Generalized Pesin-Like Identity and Scaling Relations at the Chaos Threshold of the Rossler System

In this paper, using the Poincare section of the flow we numerically verify a generalization of a Pesin-like identity at the chaos threshold of the Rossler system, which is one of the most popular three-dimensional continuous systems. As Poincare section points of the flow show similar behavior to that of the logistic map, for the Rossler system we also investigate the relationships with respect to important properties of nonlinear dynamics, such as correlation length, fractal dimension, and the Lyapunov exponent in the vicinity of the chaos threshold.