Symplectic maps are the discrete-time analog of Hamiltonian motion. They arise in many
applications including accelerator, chemical, condensed-matter, plasma, and fluid physics …

The search for chaotic patterns has occupied numerous investigators in neuroscience, as in
many other fields of science. Their results and main conclusions are reviewed in the light of …

We propose a new definition of natural invariant measure for trajectory segments of finite
duration for a many-particle system. On this basis we give an expression for the probability …

During the 1980's there were many developments regarding the nonequilibrium statistical
mechanics of dense classical atomic fluids. These developments have had a major impact …

For reversible deterministic N-particle thermostatted systems, we examine the question of
why it is so difficult to find initial microstates that will, at long times under the influence of an …

Synchronization: From Simple to Complex is devoted to the fundamental phenomenon in
physics–synchronization that occurs in coupled non-linear dissipative oscillators. Examples …

Although individual orbits of chaotic dynamical systems are by definition unpredictable, the
average behavior of typical trajectories can often be given a precise statistical description …

Pipe flow is a prominent example among the shear flows that undergo transition to
turbulence without mediation by a linear instability of the laminar profile. Experiments on …

Dynamical systems and their linear stability; 2. Topological chaos; 3. Liouvillian dynamics; 4.
Probabalistic chaos; 5. Chaotic scattering; 6. Scattering theory of transport; 7. Hydrodynamic …

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 …