From Small to Large Scales Through Dynamics Defined by Kepler Type Problems -- From Special to General Relativity Through Complex Potentials -- Geometrical and Physical Forms -- Motion on Spatial Multifractal Manifolds -- Motions on the Space-time Multifractal Manifolds -- Some Applications on Spatial Multifractal Manifolds -- Some Applications on Space-time Multifractal Manifolds.

This book aims to present the topic of nonlinear and chaotic dynamics in a manner that is useful and beneficial to students and young researchers from various domains such as physics, mathematics, biology, or even medicine. A very important aspect of that topic is that the constraints of determinism do not imply a regular behavior or do not rely on predictability in describing the dynamics of natural systems. Exploring the evolution of natural systems has a great impact nowadays on a wide range of scientific domains. The dynamics of populations, cardiac fibrillation, communication systems, fluid flow, and atmospheric systems are just a few topics in which nonlinearity and chaos are a regular manifestation. This leads to the idea that it is necessary to find universal laws that govern these dynamics. The aforementioned variety in scientific topics is also sustained by an exponential interest in recent decades from readers in the scientific community and the non-scientific one as well. The book is devoted to the nonlinear and chaotic dynamics topic, a domain that is both trans- and multi-disciplinary and has been the focus of the scientific community in past decades.