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Pressure Spectrum for Birkhoff Averages(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2012年02期
Page:
8-15
Research Field:
数学
Publishing date:

Info

Title:
Pressure Spectrum for Birkhoff Averages
Author(s):
Wang Chenwei1; Huang Ping2
1.School of Mathematical Sciences,Nanjing Normal University,Nanjing 210046,China
Keywords:
multifractal; spectrum; Birkhoff; pressure
PACS:
O174
DOI:
-
Abstract:
The strategy behind the use of Legendre transforms is to shift，from a function with one of its parameters an independent variable，to a new function with its dependence on a new variable． In this paper，we show that pressure spectra may be obtained as Legendre transforms of functions T: R→R arising in the thermodynamic formalism． The primary hypothesis we require is that the functions T be continuously differentiable． In this way we make rigorous the general paradigm of reducing questions regarding the multifractal formalism to questions regarding the thermodynamic formalism． These results hold for a broad class of measurable potentials，which includes ( but is not limited to) continuous functions．

References:

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Memo

Memo:
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Last Update: 2013-03-11