An integral formula for topological entropy of $C^{\infty}$ maps
1998 ◽
Vol 18
(2)
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pp. 405-424
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Keyword(s):
System F
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In this paper we consider a smooth dynamical system $f$ and give estimates of the growth rates of vector fields and differential forms in the $L_p$ norm under the action of the dynamical system in terms of entropy, topological pressure and Lyapunov exponents. We prove a formula for the topological entropy $$h_{\rm top}=\lim_{n\to\infty} \frac 1n \log \int \Vert Df_x^n\,^{\wedge}\Vert \,dx,$$ where $Df_x^n\,^{\wedge}$ is a mapping between full exterior algebras of the tangent spaces. An analogous formula is given for the topological pressure.
2001 ◽
Vol 129
(3)
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pp. 379-448
1978 ◽
Vol 82
(1-2)
◽
pp. 71-86
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2005 ◽
Vol 15
(04)
◽
pp. 1267-1284
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2017 ◽
Vol 448
(2)
◽
pp. 815-840
Keyword(s):