Dynamical systems, theory and applications
Abstract
The papers are devoted to the study of the time evolution of dynamical systems, encompassing finite particle systems in the classical sense, infinite systems of statistical mechanics, and wave-propagation phenomena described by nonlinear partial differential equations. A close connection is established between ergodic theory and statistical mechanics, and it is shown that striking-wave phenomena can be viewed as significant examples of integrable Hamiltonian systems of infinitely many degrees of freedom. Specific topics include the time evolution of large classical systems, ergodic properties of infinite systems, the laser as a reversible quantum dynamical system with irreversible classical macroscopic motion, geodesic flow on surfaces of negative curvature, and nonlinear wave equations. Other papers deal with integrable systems of nonlinear evolution equations, traveling-wave solutions of nonlinear diffusion equations, the existence of heteroclinic orbits, triple collision in Newtonian gravitational systems, and solutions of the collinear four-body problem which become unbounded in finite time.
- Publication:
-
Dynamical Systems, Theory and Applications
- Pub Date:
- 1975
- DOI:
- 10.1007/3-540-07171-7
- Bibcode:
- 1975LNP....38.....M
- Keywords:
-
- Conferences;
- Differential Equations;
- Dynamics;
- Ergodic Process;
- Nonlinear Equations;
- Statistical Mechanics;
- Celestial Mechanics;
- Classical Mechanics;
- Four Body Problem;
- Gravitation Theory;
- Linear Equations;
- Quantum Statistics;
- Traveling Waves;
- Wave Equations;
- Astronomy