A geometric criterion for adiabatic chaos

Journal Article · Tue Mar 01 04:00:00 EST 1994 · Journal of Mathematical Physics (New York); (United States)

DOI:https://doi.org/10.1063/1.530636· OSTI ID:5228843

Kaper, T J ^[1]; Kovacic, G ^[2]

---

1. Mathematics Department, Boston University, Boston, Massachusetts 02215 (United States)
2. Mathematical Sciences Department, Rensselaer Polytechnic Institute, Troy, New York 12180 (United States)

Chaos in adiabatic Hamiltonian systems is a recent discovery and a pervasive phenomenon in physics. In this work, a geometric criterion is discussed based on the theory of action from classical mechanics to detect the existence of Smale horseshoe chaos in adiabatic systems. It is used to show that generic adiabatic planar Hamiltonian systems exhibit stochastic dynamics in large regions of phase space. To illustrate the method, results are obtained for three problems concerning relativistic particle dynamics, fluid mechanics, and passage through resonance, results which either could not be obtained with existing methods, or which were difficult and analytically impractical to obtain with them.

• DOE Contract Number: FG02-93ER25154
• OSTI ID: 5228843
• Journal Information: Journal of Mathematical Physics (New York); (United States), Journal Name: Journal of Mathematical Physics (New York); (United States) Vol. 35:3; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACTION INTEGRAL
ADIABATIC INVARIANCE
DYNAMICS
FIELD THEORIES
FUNCTIONS
GENERAL RELATIVITY THEORY
GEOMETRY
HAMILTONIAN FUNCTION
INTEGRALS
MATHEMATICAL SPACE
MATHEMATICS
MECHANICS
MODULATION
PHASE SPACE
RELATIVITY THEORY
RESONANCE
SPACE