This pedagogical review is written as a personal retrospective which seeks to place the
celebrated Fermi, Pasta, and Ulam paradox into historical perspective. After stating the …

A brief review of the Fermi–Pasta–Ulam (FPU) paradox is given, together with its suggested
resolutions and its relation to other physical problems. We focus on the ideas and concepts …

Concepts, methods and techniques of statistical physics in the study of correlated, as well as
uncorrelated, phenomena are being applied ever increasingly in the natural sciences …

Chaos: from simple models to complex systems aims to guide science and engineering
students through chaos and nonlinear dynamics from classical examples to the most recent …

In a planetary system with two or more well-spaced, eccentric, inclined planets, secular
interactions may lead to chaos. The innermost planet may gradually become very eccentric …

In 438 alphabetically-arranged essays, this work provides a useful overview of the core
mathematical background for nonlinear science, as well as its applications to key problems …

At the present moment, after the success of the renormalization group in providing a
conceptual framework for studying second-order phase tran sitions, we have a nearly …

Phase transitions are among the most impressive phenomena occurring in nature. They are
an example of emergent behavior, ie, of collective properties having no direct counterpart in …

We study the original α-Fermi–Pasta–Ulam (FPU) system with N= 16, 32, and 64 masses
connected by a nonlinear quadratic spring. Our approach is based on resonant wave–wave …

The evolution towards equipartition in the β-FPU chain is studied considering as initial
condition the highest frequency mode. Above an analytically derived energy threshold, this …