Boc Thaler, Luka ; Fornæss, John Erik ; Peters, Han
V članku obravnavamo invariantne Fatoujeve komponente holomorfnih endomorfizmov ▫$\mathbb{P}^2$▫. Povratne Fatoujeve komponente sta klasificirala Fornæss in Sibony [Classification of recurrent ...domains for some holomorphic maps, Math.Ann. 4 (301) 1995 813-820]. Ueda je v članku [Holomorphic maps on projective spaces and continuations of, Michigan Math. J., 1(56) 2008 145-153 ] dokazal, da punktiran disk ne more biti limitna množica in s tem tudi zaključil omenjeno klasificijo. Nedavno sta Lyubich in Peters [Classification of invariant Fatou components for dissipative Hénon maps, Geom. Funct. Anal., 3 (24) 2014 887-915] klasificirala nepovratne invariantne Fatoujeve komponente, pod dodatno predpostavko, da je limitna množica enolična. Tako kot pri povratnih komponentah, so bili tudi v tej klasifikaciji znani vsi primeri razen punktiranega diska. V članku skonstruiramo preslikavo, katere limitna množica nepovratne invariantne Fatoujeve komponente je punktiran disk. S tem rezultatom tudi zaključimo klasifikacijo nepovratnih invariantnih Fatoujevih komponent v ▫$\mathbb{P}^2$▫. V nadaljevanju podamo več primerov endomorfizmov ▫$\mathbb{C}^2$▫ z nepovratnimi Fatoujevimi komponentami, na katerih orbite konvergirajo proti regularnemu delu poljubne analitične množice.
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