Attracting basins in \({\mathbb{P}}^2\)

DOI10.1007/BF02921795zbMath0982.37044OpenAlexW1997355452MaRDI QIDQ1568963

Estela Ana Gavosto

Publication date: 22 June 2000

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02921795

zbMATH Keywords

projective spaceholomorphic dynamicshomoclinic tangencyattracting basinsperiodic fixed point

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Bifurcations connected with nontransversal intersection in dynamical systems (37G25)

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Blenders near polynomial product maps of \(\mathbb{C}^2\) ⋮ Attracting currents and equilibrium measures for quasi-attractors of \(\mathbb {P}^k\) ⋮ Newhouse Laminations of polynomials on ℂ2 ⋮ Non-density of stability for holomorphic mappings on \(\mathbb{P}^k\) ⋮ Newhouse phenomenon for automorphisms of low degree in \(\mathbb{C}^3\) ⋮ Stability and bifurcations for dissipative polynomial automorphisms of \(\mathbb C^2\)

Cites Work

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• Existence of generic homoclinic tangencies for Hénon mappings
• Fatou sets in complex dynamics on projective spaces
• Classification of recurrent domains for some holomorphic maps
• Diffeomorphisms with infinitely many sinks
• Polynomial diffeomorphisms of \({\mathbb C}^2\): Currents, equilibrium measure and hyperbolicity
• Complex analytic dynamics on the Riemann sphere