相关论文: Complex dynamics and invariant forms mod p
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…
Second order integrals of motion for 3d quantum mechanical systems with position dependent masses (PDM) are classified. Namely, all PDM systems are specified which, in addition to their rotation invariance, admit at least one second order…
Invariant manifolds are important sets arising in the stability theory of dynamical systems. In this article, we take a brief review of invariant sets. We provide some results regarding the existence of invariant lines and parabolas in…
Rational maps on the Riemann sphere occupy a distinguished niche in the general theory of smooth dynamical systems. First, rational maps are complex-analytic, so a broad spectrum of techniques can contribute to their study (quasiconformal…
In this paper it is shown that Riemann invariants are invariant under nonclassical symmetries of a hyperbolic system. As a specific example, we study the one-dimensional shallow water equations on the flat and present another type…
We derive sufficient conditions for a dynamical systems to have a set of irregular points with full topological entropy. Such conditions are verified for some nonuniformly hyperbolic systems such as positive entropy surface diffeomorphisms…
Collective modes of interacting many-body systems can be related to the motion on classically invariant manifolds. We introduce suitable coordinate systems. These coordinates are Cartesian in position and momentum space. They are collective…
A key feature of a general nonlinear partially hyperbolic dynamical system is the absence of differentiability of its invariant splitting. In this paper, we show that often partial derivatives of the splitting exist and the splitting…
We show that invariant states of C*-dynamical systems can be approximated in the weak*-topology by invariant pure states, or almost invariant pure states, under various circumstances.
The complete invariant for gradient like Morse-Smale dynamical systems (vector fields and diffeomorphisms) on closed 4-manifolds are constructed. It is same as Kirby diagram in a case of polar vector field without fixed points of index 3.
Newtonian dynamical systems which accept the normal shift on an arbitrary Riemannian manifold are considered. For them the determinating equations making the weak normality condition are derived. The expansion for the algebra of tensor…
We consider integrable Hamiltonian systems in a general setting of invariant submanifolds which need not be compact. For instance, this is the case a global Kepler system, non-autonomous integrable Hamiltonian systems and integrable systems…
We consider the general model for dynamical systems defined on a simplicial complex. We describe the conjugacy classes of these systems and show how symmetries in a given simplicial complex manifest in the dynamics defined thereon,…
We completely characterize all nonlinear partial differential equations leaving a given finite-dimensional vector space of analytic functions invariant. Existence of an invariant subspace leads to a re duction of the associated dynamical…
We show that a noncommutative dynamical system of the type that occurs in quantum theory can often be associated with a dynamical principle; that is, an infinitesimal structure that completely determines the dynamics. The nature of these…
The structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group is related to a notion of Hilbert modules endowed with inner products taking values in spaces of unbounded operators. A…
We provide a new sufficient condition for strong invariance for differential inclusions, under very general conditions on the dynamics, in terms of a Hamiltonian inequality. In lieu of the usual Lipschitzness assumption on the…
Toric dynamical systems are known as complex balancing mass action systems in the mathematical chemistry literature, where many of their remarkable properties have been established. They include as special cases all deficiency zero systems…
Shape invariance is an important ingredient of many exactly solvable quantum mechanics. Several examples of shape invariant ``discrete quantum mechanical systems" are introduced and discussed in some detail. They arise in the problem of…