+*Koyama, T; *Sugano, N; *Miki, H; **Murakami, A; *Nishii, T; *Sato, Y; *Yoshikawa, H; *Tamura, S; *Ochi, T +*Osaka University Graduate School of Medicine, Osaka, Japan. [email protected] Introduction It has been reported that almost 100% of hips with extensive type of osteonecrosis of the femoral head (ONFH) show progression of collapse if they do not receive any surgical treatm...

We prove that for C generic diffeomorphisms, every expansive homoclinic class is hyperbolic.

We call a dynamical system on a measurable metric space measureexpansive if the probability of two orbits remain close each other for all time is negligible (i.e. zero). We extend results of expansive systems on compact metric spaces to the measure-expansive context. For instance, the measureexpansive homeomorphisms are characterized as those homeomorphisms f for which the diagonal is almost in...

Although Pindar's Homer began its life as the Mary Flexner Lectures in the Humanities at Bryn Mawr College in 1982, it clearly represents far more than a revised transcript of that event. The book looks more like a lifetime's work: over five hundred pages, elegantly produced with expansive footnotes and copious bibliography, wrapped in a glossy black dustjacket that gives it an authoritative, i...

Motion planning for systems with constraints on controls or the need for relatively straight paths for real-time actions presents challenges for modern planners. This paper presents an approach which addresses these types of systems by building on existing motion planning approaches. Guided Expansive Spaces Trees are introduced to search for a low cost and relatively straight path in a space wi...

We introduce the notions of weakly and strongly positively expansive (wPE and sPE, respectively) discrete dynamical systems. Both are topological generalizations of the well-known metric notion of positive expansiveness (PE). We prove that the three notions are identical on compact metrizable spaces, but not on noncompact spaces. We investigate properties of PE, wPE, and sPE dynamical systems a...