Book

Dinâmica Não Linear: Uma abordagem para economistas
(Nonlinear Dynamics: An Approach for Economists)

I am currently finishing a textbook that I have been working on for some time. My goal is to make nonlinear dynamics more accessible to economics students, particularly those who are interested in the subject but do not have a strong background in formal mathematics. The book will initially be published exclusively in Portuguese, as I particularly want to make this material accessible to students in Brazil and other Portuguese-speaking countries. This is a very personal project for me.

I grew up in Brazil and attended public schools. When I started studying economics, I had gaps in my mathematical education that made certain subjects especially difficult. Later, as I became interested in dynamical systems, I often found myself struggling not only with the mathematics itself, but also with the way it was presented. Many excellent books seemed to assume a level of mathematical preparation that I simply did not have at the time. It took me a great deal of independent study, patience, and frustration to become comfortable with ideas that I now consider fundamental to understanding economic dynamics. I still remember what it felt like to encounter a theorem without really understanding why it mattered, or to follow a proof line by line without developing any intuition for what was going on.

Those experiences have shaped the way I teach, and they are a major reason why I decided to write this book. My intention is not to avoid mathematical rigor or replace formal arguments with simplified explanations. Quite the opposite. I want to show that rigor and intuition can, and should, go together. Throughout the book, I try to introduce mathematical concepts gradually, explain the ideas behind the results, and connect them to questions that economists actually care about. Formal proofs are accompanied by intuitive discussions, and the emphasis is always on understanding the mathematics rather than simply learning how to use it.

The book moves from the foundations of dynamical systems to more advanced topics, including stability, bifurcations, chaos, stochastic dynamics, and numerical methods, with economic applications throughout. I am writing it with a particular kind of student in mind: someone who is curious, willing to work hard, and genuinely interested in mathematics, but who may feel that their previous education has not fully prepared them to enter this field. I know that feeling very well, and I hope this book can make that path a little less difficult for others than it was for me.

The manuscript is now in its final stages of preparation, and I hope to make it available in the near future. It has been a demanding project, but also one of the most meaningful things I have worked on.