Reducible Dehn Surgery and Toroidal Dehn Surgery

Let M be a compact, orientable, irreducible ,irreducible, atoroidal, anannular 3-manifold with one component T0 of M a torus. Suppose that r1 and r2 are two slopes on T0 In this paper,we prove that 1) if M(r1) is reducible while M(r2) contains an essential torus, then Δ(r1,r2)≤4;2) if M(r1) is reducible while M(r2) contains an essential torus, then Δ(r1,r2)≤4.     

进位吸引子与拓扑熵

Let M be a manifold (possibly with boundary), and f:M→M be continuous. Call a closed invariant set A包含M an adic attractor of f if it attracts almost all points (in the sense of Lebesgue measure) and the restriction f|A is topologically conjugate to an adic system. Such an attractor A is called n-adic if the restriction flA can be topologically conjugate the n-adic system.