Scale Invariance in Nonlinear Dynamical Systems
暫譯: 非線性動態系統中的尺度不變性

Edson Denis Leonel is a Professor of Physics at São Paulo State University (UNESP), Rio Claro, Brazil. He has been working on scaling investigations since his Ph.D. in 2003, where he conducted the first study of scaling behavior in the chaotic sea of the Fermi-Ulam model. His research group has developed a variety of approaches and formalisms to investigate and characterize scaling properties across a wide range of systems, including one-dimensional mappings, ordinary differential equations, cellular automata, meme propagation, and time-dependent billiards. His group has investigated different types of transitions in using scaling investigations, including but not limited to: (i) the transition from integrability to non-integrability; (ii) the transition from limited to unlimited diffusion; and (iii) the production and suppression of Fermi acceleration - the latter involving the analytical solution of the diffusion equation. Professor Leonel and his collaborators have published more than 180 scientific papers in respected international journals, including three in Physical Review Letters. He is the author of Scaling Laws in Dynamical Systems (Springer & Higher Education Press, 2021), and Dynamical Phase Transitions in Chaotic Systems (Springer & Higher Education Press, 2023) as well as two books in Portuguese: one on Statistical Mechanics (Blucher, 2015) and another on Nonlinear Dynamics (Blucher, 2019).

Edson Denis Leonel 是巴西里約克拉羅的聖保羅州立大學（UNESP）物理學教授。他自2003年獲得博士學位以來，一直從事縮放研究，並在該年進行了Fermi-Ulam模型混沌海洋中縮放行為的首次研究。他的研究團隊開發了多種方法和形式主義，以調查和特徵化各種系統的縮放性質，包括一維映射、常微分方程、元胞自動機、迷因傳播和時間依賴的撞球。他的團隊利用縮放研究調查了不同類型的轉變，包括但不限於：(i) 從可積分性到不可積分性的轉變；(ii) 從有限擴散到無限擴散的轉變；以及 (iii) Fermi加速的產生和抑制 - 後者涉及擴散方程的解析解。Leonel教授及其合作者在國際知名期刊上發表了超過180篇科學論文，其中包括三篇發表在《Physical Review Letters》上的論文。他是《動態系統中的縮放法則》（Springer & Higher Education Press, 2021）和《混沌系統中的動態相變》（Springer & Higher Education Press, 2023）的作者，並且還有兩本葡萄牙語書籍：一本關於統計力學（Blucher, 2015）和另一本關於非線性動力學（Blucher, 2019）。