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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2010/323069 |
| Summary: | <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> |
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| ISSN: | 1687-1820 1687-1812 |