Jerrold E. Marsden, 1942-2010

Jerry Marsden, one of the world's pre-eminent mechanicians and applied mathematicians, died on September 21st, 2010 after a 12-year battle with cancer. Phil Holmes and Richard Murray commemorate Jerry.

In the memory of Jaroslav Stark, 17 June 1960 – 6 June 2010

Jaroslav Stark commemorated by Paul Glendinning. This will be published in the August 2010 issue of 'Mathematics Today', the IMA's members publication.

To the Memory of Jack K. Hale (1928-2009)

"In the Emory Hospital of Atlanta, in the early morning of December 9, 2009, there passed away a great man, Jack K. Hale -- a founding father of numerous areas of modern dynamics, a noble scholar and teacher, and a mentor and dear friend of many of us around the world."
In this article Jack is commemorated by Yingfei Yi, who also interviewed him in 2003 for DSWeb Magazine.

The Rise, Fall, and Legacy of Catastrophe Theory

In the 2009 Moser Lecture, titled “Catastrophes, Symmetry-Breaking, Synchrony-Breaking,” Golubitsky surveyed the rise, fall, and legacy of catastrophe theory. In particular, he showed how some of the ideas of catastrophe theory can be applied to study the dynamics of networks.

Crawford prize winners revisited: Björn Sandstede

The Crawford prize is awarded biannually since 2001 at the `Snowbird' conferences by the SIAM activity group on dynamical systems for recent outstanding work on a topic in nonlinear science. In a planned series of articles we invite the winners to write about their mathematical biography, their work, and what they consider important problems in the field of applied dynamical system. This article contains the contribution of the first prize winner Björn Sandstede.

Homology: An Idea Whose Time Has Come

Tools from the purportedly abstract field of algebraic topology are finding their way into applied mathematics, and Robert Ghrist of the University of Pennsylvania is helping lead the invasion. Ghrist and colleagues use ideas from homology to solve perplexing problems arising in sensor networks, helping to improve their coverage, robustness, and efficiency.

Leading indicators of critical transitions: theory or practice?

Vasilis Dakos, Egbert van Nes, and Marten Scheffer summarize their recent results published in Nature on early-warning signals for critical transitions in a variety of systems ranging from fisheries to climate to financial markets.

Why Do Math

Inspired by the frequent need to answer the question, Why Do Math is a SIAM-sponsored website highlighting many of the exciting contributions made by computational science and mathematics to science, society, and everyday life. Though not specifically about dynamical systems, it includes many dynamical systems related topics (several of which are linked in the DSWeb Tutorials Section). The website is currently under development, but a number of tutorials are already available for view, on The America's Cup, Coclear Implants, Mathematics of Neuroscience, Space Travel, Tomography, Voting, and Wavelets.

Finding Appropriate Dynamics for the Social Sciences

The growing area of "mathematical social sciences" has provided valued insights for several disciplines, but a key aspect of this development desperately needs help from mathematicians who are skilled in dynamical systems. Namely, although "change" obviously is a central feature for all of the social sciences, it is not clear how it should be modeled. Indeed, in a real sense, this article is a call for help; it is an appeal for more people from the dynamical systems community to become involved. What makes the challenge attractive is that, once the appropriate dynamics are discovered, they most surely will involve features that differ from what we currently see in the literature. To introduce what causes some of the complexities of these areas, results and difficulties associated with price dynamics are described. As it will become clear, much less is known about how prices change than the reader might have expected.