We develop a generalized multifractal analysis based on the Legendre-Fenchel transform instead of the routinely used Legendre transform. We test this analysis for study time series consisting of interevent times. As a result, we have received the nonmonotonic behavior of the generalized Hurst exponent (which is a basic exponent herein) and hence a multi-branched left-sided spectrum of dimensions. This kind of multifractality is a direct result of the nonmonotonic behavior of the generalized Hurst exponent and not because of its non-analytic behavior as it found before. We have examined 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 as well as to first and the second order phase transitions between them.
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.
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a generalized
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instead of
rather than
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test this analysis for study
apply this analysis to studying
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have received the nonmonotonic
discern the non-monotonic
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(which is a basic exponent herein)
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nonmonotonic
non-monotonic
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not because of its
is not caused by
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it found before. We have examined
has been previously suggested. We examine
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