Title: New face of multifractality: Multi-branched left-sidedness and phase transitions in multifractality of interevent times,
Abstract: We develop an extended multifractal analysis based on the Legendre-Fenchel
transform rather than the routinely used Legendre transform. We apply this
analysis to studying time series consisting of inter-event times. As a result,
we discern the non-monotonic behavior of the generalized Hurst exponent - the
fundamental exponent studied by us - and hence a multi-branched left-sided
spectrum of dimensions. This kind of multifractality is a direct result of the
non-monotonic behavior of the generalized Hurst exponent and is not caused by
non-analytic behavior as has been previously suggested. We examine the main
thermodynamic consequences of the existence of this type of multifractality
related to the thermal stable, metastable, and unstable phases within a
hierarchy of fluctuations, and also to the first and second order phase
transitions between them.