This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

chapter 1|12 pages


part |2 pages

Part I One-Dimensional Flows

chapter 2|30 pages

Flows on the Line

chapter 3|50 pages


chapter 4|28 pages

Flows on the Circle

part |2 pages

Part II Two-Dimensional Flows

chapter 5|21 pages

Linear Systems

chapter 6|52 pages

Phase Plane

chapter 7|46 pages

Limit Cycles

chapter 8|67 pages

Bifurcations Revisited

part |2 pages

Part III Chaos

chapter 9|46 pages

Lorenz Equations

chapter 10|50 pages

One-Dimensional Maps

chapter 11|24 pages


chapter 12|31 pages

Strange Attractors