Timeline for Shub Conjecture and polynomial entropy
Current License: CC BY-SA 4.0
11 events
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| Jul 10 at 16:21 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Jul 10 at 8:59 | comment | added | Ali Taghavi | @JohnB As you pointed out, my motivation for this question was just zero entropy maps | |
| Jul 10 at 1:42 | comment | added | John B | There is nothing to expand in my comment, sorry, it is only my answer to your question "Are there ..." I have never seen it written anywhere and yes, of course, $\log n$ can be replaced by any other rate. Is this interesting? Maybe, probably not (but if so it could perhaps help understanding the dynamics of zero entropy maps). It is doubtful for example that Yomdin's proof for $C^\infty$ maps extends to other growth rates (sorry, too technical to explain here why). | |
| Jul 9 at 21:27 | comment | added | Ali Taghavi | @JohnB BTW in the question I did not say that we formally replace topological entropy with polynomial one(without any other possible change). I would appreciate if you read my question again | |
| Jul 9 at 21:17 | comment | added | Ali Taghavi | @JohnB are there examples of non vanishing of the induced homology map $f_*$ but the topological entropy $h(f)=0$? | |
| Jul 9 at 21:15 | comment | added | Ali Taghavi | @JohnB Please expand your comment | |
| Jul 9 at 20:49 | comment | added | Ali Taghavi | @JohnB Thank you! are there some dynamical interpretations for this spectrum condition? | |
| Jul 9 at 20:40 | comment | added | John B | You would replace the exponential growth rate for the action on the homology by the new growth rate: look at the limits of $\|f_*^n\|/\log n$. But it is only of interest if the spectrum of $f_*$ is contained in the imaginary axis. | |
| Jul 9 at 20:20 | history | edited | Ali Taghavi |
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| Jul 9 at 19:44 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Jul 9 at 19:39 | history | asked | Ali Taghavi | CC BY-SA 4.0 |