20.500.12556/DKUM-100500 The center problem for analytic maps with mixed even-degree terms 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. discrete dynamical systems center variety analytic maps Poincaré return map diskretni dinamični sistemi množica centrov analitične preiskave Poincaréjeva povratna preslikava true false true MDPI Angleški jezik Slovenski jezik https://www.mdpi.com/journal/axioms Članek v reviji 2026-09-21 10:26:16 2026-09-21 10:26:17 2026-09-22 03:08:07 0000-00-00 00:00:00 2026 0 0 12 str. issue 9, [article no.] 669 Vol. 15 Sep. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2026-07-28 2026-08-24 2026-09-07 517.9 291745027 10.3390/axioms15090669 2075-1680 axioms-15-00669.pdf axioms-15-00669.pdf 1 C7D6AF20670663970F9A86F99E6A08E9 3aefefb1935c8e284af43d4e784c023d892f91045160bf63eba94c79a8da8516 d454b4a1-b596-11f1-a810-00155d0001be https://dk.um.si/Dokument.php?lang=slv&id=213012 https://www.mdpi.com/2075-1680/15/9/669 1 1e17c5c7-b596-11f1-a810-00155d0001be https://dk.um.si/Dokument.php?lang=slv&id=213011 Fakulteta za naravoslovje in matematiko Fakulteta za energetiko Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo 0 0 0