Dynamical Phase Transitions in Chaotic Systems is popular PDF and ePub book, written by Edson Denis Leonel in 2023-08-14, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Dynamical Phase Transitions in Chaotic Systems can be Read Online from any device for your convenience.
Dynamical Phase Transitions in Chaotic Systems Book PDF Summary
This book discusses some scaling properties and characterizes two-phase transitions for chaotic dynamics in nonlinear systems described by mappings. The chaotic dynamics is determined by the unpredictability of the time evolution of two very close initial conditions in the phase space. It yields in an exponential divergence from each other as time passes. The chaotic diffusion is investigated, leading to a scaling invariance, a characteristic of a continuous phase transition. Two different types of transitions are considered in the book. One of them considers a transition from integrability to non-integrability observed in a two-dimensional, nonlinear, and area-preserving mapping, hence a conservative dynamics, in the variables action and angle. The other transition considers too the dynamics given by the use of nonlinear mappings and describes a suppression of the unlimited chaotic diffusion for a dissipative standard mapping and an equivalent transition in the suppression of Fermi acceleration in time-dependent billiards. This book allows the readers to understand some of the applicability of scaling theory to phase transitions and other critical dynamics commonly observed in nonlinear systems. That includes a transition from integrability to non-integrability and a transition from limited to unlimited diffusion, and that may also be applied to diffusion in energy, hence in Fermi acceleration. The latter is a hot topic investigated in billiard dynamics that led to many important publications in the last few years. It is a good reference book for senior- or graduate-level students or researchers in dynamical systems and control engineering, mathematics, physics, mechanical and electrical engineering.
Detail Book of Dynamical Phase Transitions in Chaotic Systems PDF
- Author : Edson Denis Leonel
- Release : 14 August 2023
- Publisher : Springer Nature
- ISBN : 9789819922444
- Genre : Mathematics
- Total Page : 83 pages
- Language : English
- PDF File Size : 19,8 Mb
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