Topic
Dynamical system (definition)
About: Dynamical system (definition) is a research topic. Over the lifetime, 1778 publications have been published within this topic receiving 35199 citations.
Papers published on a yearly basis
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Papers
TL;DR: In this article, it was shown that it is possible to build up a fairly satisfactory theory of the emission of radiation and of the reaction of the radiation field on the emitting system on the basis of a kinematics and dynamics which are not strictly relativistic.
Abstract: The new quantum theory, based on the assumption that the dynamical variables do not obey the commutative law of multiplication, has by now been developed sufficiently to form a fairly complete theory of dynamics. One can treat mathematically the problem of any dynamical system composed of a number of particles with instantaneous forces acting between them, provided it is describable by a Hamiltonian function, and one can interpret the mathematics physically by a quite definite general method. On the other hand, hardly anything has been done up to the present on quantum electrodynamics. The questions of the correct treatment of a system in which the forces are propagated with the velocity of light instead of instantaneously, of the production of an electromagnetic field by a moving electron, and of the reaction of this field on the electron have not yet been touched. In addition, there is a serious difficulty in making the theory satisfy all the requirements of the restricted principle of relativity, since a Hamiltonian function can no longer be used. This relativity question is, of course, connected with the previous ones, and it will be impossible to answer any one question completely without at the same time answering them all. However, it appears to be possible to build up a fairly satisfactory theory of the emission of radiation and of the reaction of the radiation field on the emitting system on the basis of a kinematics and dynamics which are not strictly relativistic.
2,245 citations
TL;DR: In this article, a general algorithm for constructing coherent states of dynamical groups for a given quantum physical system is presented, and the result is that the coherent states are isomorphic to a coset space of group geometrical space.
Abstract: In this review, a general algorithm for constructing coherent states of dynamical groups for a given quantum physical system is presented. The result is that, for a given dynamical group, the coherent states are isomorphic to a coset space of group geometrical space. Thus the topological and algebraic structure of the coherent states as well as the associated dynamical system can be extensively discussed. In addition, a quantum-mechanical phase-space representation is constructed via the coherent-state theory. Several useful methods for employing the coherent states to study the physical phenomena of quantum-dynamic systems, such as the path integral, variational principle, classical limit, and thermodynamic limit of quantum mechanics, are described.
1,688 citations
TL;DR: In this article, a definition for the concept of "attractor" was proposed based on the probable asymptotic behavior of orbits, and the definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor.
Abstract: This note proposes a definition for the concept of “attractor,” based on the probable asymptotic behavior of orbits. The definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor.
1,134 citations
TL;DR: This chapter shows how the theory of stochastic dynamical systems can be used to characterize the equilibria that are most likely to be selected when the evolutionary process is subject to small persistent perturbations, said to be stochastically stable.
1,126 citations
TL;DR: It is proved that any finite time trajectory of a given n-dimensional dynamical system can be approximately realized by the internal state of the output units of a continuous time recurrent neural network with n output units, some hidden units, and an appropriate initial condition.
1,111 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 17 |
| 2024 | 26 |
| 2023 | 76 |
| 2022 | 209 |
| 2021 | 110 |
| 2020 | 88 |