| Naslov: | The center problem for analytic maps with mixed even-degree terms |
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| Avtorji: | ID Petek, Renato (Avtor)
ID Ferčec, Brigita (Avtor)
ID Fernandes, Wilker (Avtor)
ID Mencinger, Matej (Avtor) |
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| Datoteke: |  axioms-15-00669.pdf (269,35 KB)
MD5: C7D6AF20670663970F9A86F99E6A08E9
 https://www.mdpi.com/2075-1680/15/9/669
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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: | FNM - Fakulteta za naravoslovje in matematiko
FE - Fakulteta za energetiko
FGPA - Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo
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| Opis: | We investigate the center problem for analytic maps implicitly defined by algebraic equations of the form F(x, y) = x + y + ∑ i+k=2αi,kxiyk = 0. Previous studies of homogeneous analytic maps of even degree and of mixed terms of degrees 2 and 4 revealed two recurring algebraic families characterizing the existence of a center at the origin: mirror-symmetry conditions and alternating-sum conditions. In this paper, we resolve the next open case involving mixed terms of degrees 2 and 6 and show that the same algebraic structure extends to mixed terms of degrees 2 and arbitrary even number. Using an approach based on the involutive identity f ( f (x)) = x, we prove that these two families of algebraic conditions completely characterize the existence of a center at the origin. The proof combines algebraic and structural arguments and avoids the use of explicit higher-order focus quantity computations in the general case. |
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| Ključne besede: | discrete dynamical systems, center variety, analytic 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: | 28.07.2026 |
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| Datum sprejetja članka: | 24.08.2026 |
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| Datum objave: | 07.09.2026 |
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| Založnik: | MDPI |
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| Leto izida: | 2026 |
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| Št. strani: | 12 str. |
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| Številčenje: | Vol. 15, issue 9, [article no.] 669 |
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| PID: | 20.500.12556/DKUM-100500  |
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| UDK: | 517.9 |
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| COBISS.SI-ID: | 291745027 |
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| DOI: | 10.3390/axioms15090669 |
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| ISSN pri članku: | 2075-1680 |
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| Datum objave v DKUM: | 21.09.2026 |
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| Število ogledov: | 123 |
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| Število prenosov: | 3 |
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| Metapodatki: |    |
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| Področja: | Ostalo
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