We prove the Ingram conjecture, ie we show that the inverse limit spaces of tent maps with different slopes in the interval OE1; 2 are nonhomeomorphic. Based on the structure obtained from the proof, we also show that every self-homeomorphism of the inverse limit space of a tent map is pseudo-isotopic, on the core, to some power of the shift homeomorphism. 54H20; 37B45, 37E05
In this paper we prove the nonrecurrent case of the Ingram conjecture by showing that if T s and T t are two tent maps with nonrecurrent critical points then lim fOE0; 1; T s g is homeomorphic to lim fOE0; 1; T t g if and only if s D t .
37B10; 37B45
In this paper we study the family of the Lozi maps L a,b : R 2 → R 2 , L a,b = (1+y−a|x|, bx), and their strange attractors Λ a,b . We introduce the set of kneading sequences for the Lozi map and prove that it determines the symbolic dynamics for that map. We also introduce two other equivalent approaches.
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