| Naslov: | The center problem for homogeneous case of polynomial maps |
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| Avtorji: | ID Petek, Renato (Avtor)
ID Ferčec, Brigita (Avtor)
ID Mencinger, Matej (Avtor) |
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| Datoteke: |  axioms-15-00370.pdf (275,11 KB)
MD5: 0F1FD3B9742B60C49A00024EA3F14741
 https://www.mdpi.com/2075-1680/15/5/370
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| Jezik: | Angleški jezik |
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| Vrsta gradiva: | Članek v reviji |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: | FGPA - Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo
FE - Fakulteta za energetiko
FNM - Fakulteta za naravoslovje in matematiko
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| Opis: | We study the center problem for polynomial maps y=�(�)=−�−∑�=1∞����+1, arising from homogeneous algebraic curves �+�+∑�=0���−�,���−���=�+�+��(�,�)=0. While explicit conditions were previously known only for low even degrees �=2,4,6,8,10 , their general structure remained conjectural. In this paper we resolve the case �=12 and prove that for all even degrees �=2� , the center condition is completely characterized by two families of algebraic relations: mirror symmetry conditions and alternating-sum conditions. The proof combines algebraic methods with a direct structural argument. In particular, the necessity part is established without relying on explicit formulas for focus quantities, instead, we make use of the involutive property of the associated map and analyze the symmetric difference ��(�,�(�))−��(�(�),�), which leads to a simple and rigorous characterization of the center condition. This provides a complete and conceptually transparent solution of the homogeneous center problem for polynomial maps. |
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| Ključne besede: | discrete dynamical systems, center variety, polynomial maps, Poincaré return map |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Poslano v recenzijo: | 01.04.2026 |
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| Datum sprejetja članka: | 13.05.2026 |
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| Datum objave: | 15.05.2026 |
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| Založnik: | MDPI |
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| Leto izida: | 2026 |
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| Št. strani: | 11 str. |
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| Številčenje: | Vol. 15, issue 5, [article no.] 370 |
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| PID: | 20.500.12556/DKUM-98229  |
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| UDK: | 517.9 |
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| COBISS.SI-ID: | 279685635 |
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| DOI: | 10.3390/axioms15050370 |
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| ISSN pri članku: | 2075-1680 |
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| Datum objave v DKUM: | 28.05.2026 |
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| Število ogledov: | 180 |
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| Število prenosov: | 10 |
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| Metapodatki: |    |
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| Področja: | Ostalo
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