"Butterfly Effect" vs Chaos in Energy Futures Markets
  In this paper we test for the sensitive dependence on initial conditions (the so called "butterfly effect") of energy futures time series (heating oil, natural gas), and thus the determinism of those series. This paper is distinguished from previous studies in the following points: first, we reread existent works in the literature on energy markets, enlightening the role of \emph{butterfly effect} in chaos definition (introduced by Devaney), using this definition to prevent us from misleading results about ostensible chaoticity of the price series. Second, we test for the time series for sensitive dependence on initial conditions, introducing a coefficient that describes the determinism rate of the series and that represents its reliability level (in percentage). The introduction of this reliability level is motivated by the fact that time series generated from stochastic systems also might show sensitive dependence on initial conditions. According to this perspective, the maximum reliability level obtained here is too low to be able to ensure that there is strong evidence of sensitive The maximum reliability level obtained here was been $\simeq 56\% $, too low to ensure strong evidence of sensitive dependence on initial conditions. 
Loretta Mastroeni and Pierluigi Vellucci
q-fin.ST