C. Hinsley

26 June 2024

These are just some books and papers I found useful or unusually comprehensive while digging around and thinking about iterated continuous maps on real intervals. There is also some work by Avrutin, Sushko, and some others on discontinuous such maps.

• Welington de Melo, Sebastian van Strien - One-Dimensional Dynamics
• John Milnor, William (Bill) Thurston - On Iterated Maps of the Interval (Kneading Invariants Theory)
• Sylvie Ruette - Chaos on the Interval
• Oleksandr Sharkovsky - Sharkovsky ordering
• Michael Benedicks, Michal Misiurewicz - Absolutely continuous invariant measures for maps with flat tops
• Louis Block, John Guckenheimer, Michal Misiurewicz, Lai Sang Young - Periodic points and topological entropy of one dimensional maps
• Alseda, Llibre, Misiurewicz - Combinatorial Dynamics and Entropy
• Jose Amigo, Angel Gimenez - A Simplified Algorithm for the Topological Entropy of Multimodal Maps
• Henk Bruin, Sebastian van Strien - Monotonicity of Entropy for Real Multimodal Maps
• Jose Amigo, Rui Dilao, Angel Giminez - Computing the Topological Entropy of Multimodal Maps via Min-Max Sequences
• Douglas Lind, Brian Marcus - Symbolic Dynamics and Coding
• William Thurston - Entropy in Dimension One
• Lluis Alseda, Jozef Bobek, Michal Misiurewicz, Lubomir Snoha - The Real Teapot
• V. V. Fedorenko, A. N. Sharkovsky - On coexistence of homoclinic and periodic trajectories This one describes a condition for finding 1-homoclinics in maps. There is an English version of this floating around somewhere, but it may have a slightly different name.
• Viktor Avrutin, Björn Schenke, Laura Gardini - Calculation of homoclinic and heteroclinic orbits in 1D maps
• Pierre Collet, Jean-Pierre Eckmann - Iterated Maps on the Interval as Dynamical Systems