A Poincaré Formula for the Fixed Point Indices of the Iterates of Arbitrary Planar Homeomorphisms
<p>Abstract</p> <p>Let <inline-formula> <graphic file="1687-1812-2010-323069-i1.gif"/></inline-formula> be an open subset and <inline-formula> <graphic file="1687-1812-2010-323069-i2.gif"/></inline-formula> be an arbitrary loc...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2010-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2010/323069 |
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doaj-dcd6f0caa3c44b45b5dc2158a39f82922020-11-25T01:03:37ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122010-01-0120101323069A Poincaré Formula for the Fixed Point Indices of the Iterates of Arbitrary Planar HomeomorphismsSalazar JoséMRuiz del Portal FranciscoR<p>Abstract</p> <p>Let <inline-formula> <graphic file="1687-1812-2010-323069-i1.gif"/></inline-formula> be an open subset and <inline-formula> <graphic file="1687-1812-2010-323069-i2.gif"/></inline-formula> be an arbitrary local homeomorphism with <inline-formula> <graphic file="1687-1812-2010-323069-i3.gif"/></inline-formula>. We compute the fixed point indices of the iterates of <inline-formula> <graphic file="1687-1812-2010-323069-i4.gif"/></inline-formula> at <inline-formula> <graphic file="1687-1812-2010-323069-i5.gif"/></inline-formula>, and we identify these indices in dynamical terms. Therefore, we obtain a sort of Poincaré index formula without differentiability assumptions. Our techniques apply equally to both orientation preserving and orientation reversing homeomorphisms. We present some new results, especially in the orientation reversing case.</p>http://www.fixedpointtheoryandapplications.com/content/2010/323069 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Salazar JoséM Ruiz del Portal FranciscoR |
| spellingShingle |
Salazar JoséM Ruiz del Portal FranciscoR A Poincaré Formula for the Fixed Point Indices of the Iterates of Arbitrary Planar Homeomorphisms Fixed Point Theory and Applications |
| author_facet |
Salazar JoséM Ruiz del Portal FranciscoR |
| author_sort |
Salazar JoséM |
| title |
A Poincaré Formula for the Fixed Point Indices of the Iterates of Arbitrary Planar Homeomorphisms |
| title_short |
A Poincaré Formula for the Fixed Point Indices of the Iterates of Arbitrary Planar Homeomorphisms |
| title_full |
A Poincaré Formula for the Fixed Point Indices of the Iterates of Arbitrary Planar Homeomorphisms |
| title_fullStr |
A Poincaré Formula for the Fixed Point Indices of the Iterates of Arbitrary Planar Homeomorphisms |
| title_full_unstemmed |
A Poincaré Formula for the Fixed Point Indices of the Iterates of Arbitrary Planar Homeomorphisms |
| title_sort |
poincaré formula for the fixed point indices of the iterates of arbitrary planar homeomorphisms |
| publisher |
SpringerOpen |
| series |
Fixed Point Theory and Applications |
| issn |
1687-1820 1687-1812 |
| publishDate |
2010-01-01 |
| description |
<p>Abstract</p> <p>Let <inline-formula> <graphic file="1687-1812-2010-323069-i1.gif"/></inline-formula> be an open subset and <inline-formula> <graphic file="1687-1812-2010-323069-i2.gif"/></inline-formula> be an arbitrary local homeomorphism with <inline-formula> <graphic file="1687-1812-2010-323069-i3.gif"/></inline-formula>. We compute the fixed point indices of the iterates of <inline-formula> <graphic file="1687-1812-2010-323069-i4.gif"/></inline-formula> at <inline-formula> <graphic file="1687-1812-2010-323069-i5.gif"/></inline-formula>, and we identify these indices in dynamical terms. Therefore, we obtain a sort of Poincaré index formula without differentiability assumptions. Our techniques apply equally to both orientation preserving and orientation reversing homeomorphisms. We present some new results, especially in the orientation reversing case.</p> |
| url |
http://www.fixedpointtheoryandapplications.com/content/2010/323069 |
| work_keys_str_mv |
AT salazarjos233m apoincar233formulaforthefixedpointindicesoftheiteratesofarbitraryplanarhomeomorphisms AT ruizdelportalfranciscor apoincar233formulaforthefixedpointindicesoftheiteratesofarbitraryplanarhomeomorphisms AT salazarjos233m poincar233formulaforthefixedpointindicesoftheiteratesofarbitraryplanarhomeomorphisms AT ruizdelportalfranciscor poincar233formulaforthefixedpointindicesoftheiteratesofarbitraryplanarhomeomorphisms |
| _version_ |
1715865138436767744 |