On (non-)local-connectivity of some Julia sets

Alexandre Dezotti (1) , Pascale Roesch (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 I2M - Institut de Mathématiques de Marseille

This article deals with the question of local connectivity of the Julia set of polynomials and rational maps. It essentially presents conjectures and questions.

Domaines: Systèmes dynamiques [math.DS]; Variables complexes [math.CV]

Alexandre Dezotti, Pascale Roesch. On (non-)local-connectivity of some Julia sets. Frontiers in complex dynamics, 51, Princeton Univ. Press, Princeton, NJ, pp.135--162, 2014, Princeton Math. Ser., ⟨10.1515/9781400851317-010⟩. ⟨hal-01313120⟩