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- W2001685372 abstract "We study the differentiability properties of the pre-image pressure. For a TDS<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:math>with finite topological pre-image entropy, we prove the pre-image pressure function<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mtext>p</mml:mtext><mml:mtext>r</mml:mtext><mml:mtext>e</mml:mtext></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:mo>•</mml:mo><mml:mo>)</mml:mo></mml:math>is Gateaux differentiable at<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>f</mml:mi><mml:mo>∈</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant=double-struck>R</mml:mi><mml:mo>)</mml:mo></mml:math>if and only if<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mtext>p</mml:mtext><mml:mtext>r</mml:mtext><mml:mtext>e</mml:mtext></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:mo>•</mml:mo><mml:mo>)</mml:mo></mml:math>has a unique tangent functional at<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>f</mml:mi></mml:math>. Also, we obtain some equivalent conditions for<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mtext>p</mml:mtext><mml:mtext>r</mml:mtext><mml:mtext>e</mml:mtext></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:mo>•</mml:mo><mml:mo>)</mml:mo></mml:math>to be Fréchet differentiable at<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>f</mml:mi></mml:math>." @default.
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- W2001685372 date "2012-01-01" @default.
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- W2001685372 title "Differentiability Properties of the Pre-Image Pressure" @default.
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