Feigenbaum graphs at the onset of chaos

Article history: Received 11 July 2012 Received in revised form 9 October 2012 Accepted 30 October 2012 Available online 5 November 2012 Communicated by C.R. Doering We analyze the properties of networks obtained from the trajectories of unimodal maps at the transition to chaos via the horizontal visibility (HV) algorithm. We find that the network degrees fluctuate at all scales with amplitude that increases as the size of the network grows, and can be described by a spectrum of graph-theoretical generalized Lyapunov exponents. We further define an entropy growth rate that describes the amount of information created along paths in network space, and find that such entropy growth rate coincides with the spectrum of generalized graph-theoretical exponents, constituting a set of Pesin-like identities for the network. © 2012 Elsevier B.V. All rights reserved.