| Title:
|
$C^1$ self-maps on closed manifolds with finitely many periodic points all of them hyperbolic (English) |
| Author:
|
Llibre, Jaume |
| Author:
|
Sirvent, Víctor F. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
141 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
83-90 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a connected closed manifold and $f$ a self-map on $X$. We say that $f$ is almost quasi-unipotent if every eigenvalue $\lambda $ of the map $f_{*k}$ (the induced map on the \mbox {$k$-th} homology group of $X$) which is neither a root of unity, nor a zero, satisfies that the sum of the multiplicities of $\lambda $ as eigenvalue of all the maps $f_{*k}$ with $k$ odd is equal to the sum of the multiplicities of $\lambda $ as eigenvalue of all the maps $f_{*k}$ with $k$ even. \endgraf We prove that if $f$ is $C^1$ having finitely many periodic points all of them hyperbolic, then $f$ is almost quasi-unipotent. (English) |
| Keyword:
|
hyperbolic periodic point |
| Keyword:
|
differentiable map |
| Keyword:
|
Lefschetz number |
| Keyword:
|
Lefschetz zeta function |
| Keyword:
|
quasi-unipotent map |
| Keyword:
|
almost quasi-unipotent map |
| MSC:
|
37C05 |
| MSC:
|
37C25 |
| MSC:
|
37C30 |
| idZBL:
|
Zbl 06562160 |
| idMR:
|
MR3475139 |
| DOI:
|
10.21136/MB.2016.6 |
| . |
| Date available:
|
2016-03-17T19:47:58Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144853 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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