Focused on the theory of chaotic maps in finite-dimensional spaces, this book is structured around lecture notes from a graduate course. It includes ten chapters that explore one-dimensional dynamical systems, bifurcations, symbolic dynamics, and fractals, along with a novel perspective on rapid fluctuations in chaotic maps. Two appendices facilitate the transition from discrete to continuous-time dynamical systems, covering ordinary and partial differential equations. The comprehensive content is suitable for readers seeking a foundational understanding of dynamical systems and chaos.
Through application of the Smoothed Particle Hydrodynamics (SPH) method, this monograph mainly focuses on large deformations and flow failure simulations of geomaterials and movement behavior, which are always involved in geo-disasters. The work covers the theoretical background, numerical techniques, code implementation issues, and many novel and interesting applications. Two-dimensional and three-dimensional SPH models in the framework of both hydrodynamics and solid mechanics are established, with detailed descriptions. The monograph also contains many appealing and practical examples of geo-disaster modeling and analysis, including the fluidized movement of flow-like landslides, lateral spread of liquefied soils, and flow slides in landfills. In the documented SPH simulations, the propagation of geo-disasters is effectively reproduced. Dynamic behaviors of geomaterials during propagation are ascertained, including sliding path, flow velocity, maximum distance reached, and distribution of deposits. In this way, the monograph presents a means for mapping hazardous areas, estimating hazard intensity, and identifying and designing appropriate protective measures.
