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伯克霍夫平均的压谱(英文)(
)
《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]
- 卷:
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第35卷
- 期数:
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2012年02期
- 页码:
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8-15
- 栏目:
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数学
- 出版日期:
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2012-06-20
文章信息/Info
- Title:
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Pressure Spectrum for Birkhoff Averages
- 作者:
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王琛玮1; 黄萍2
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( 1． 南京师范大学数学科学学院，江苏南京210046) ( 2． 解放军理工大学理学院，江苏南京211101)
- Author(s):
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Wang Chenwei1; Huang Ping2
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1.School of Mathematical Sciences,Nanjing Normal University,Nanjing 210046,China
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- 关键词:
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- Keywords:
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- 分类号:
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O174
- 摘要:
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Legendre变换的作用是将一个独立参变量函数转化为一个新的独立参变量函数.本文证明了在热力学形式中压谱可以由函数T:R→R的Legendre变换所获得.所考虑的函数T为连续可微.用这种方法我们将重分形的问题转化为热力学问题,这些结果对更广一类的可测函数仍成立,包含了(而不仅限于)连续函数.
- Abstract:
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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．
更新日期/Last Update:
2013-03-11