相关论文: Characterisation of Log-Convex Decay in Non-Selfad…

In the framework of the generalized Hamiltonian formalism by Dirac, the local symmetries of dynamical systems with first- and second-class constraints are investigated in the general case without restrictions on the algebra of constraints.…

Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…

Hamiltonian time evolution in terms of an explicit parameter time is derived for general relativity, even when the constraints are not satisfied, from the Arnowitt-Deser-Misner-Teitelboim-Ashtekar action in which the slicing density…

In a previous work, the author established a nonautonomous Conley index based on the interplay between a nonautonomous evolution operator and its skew-product formulation. This index is refined to obtain a Conley index for families of…

We discuss linear autonomous evolution equations on function spaces which have the property that a positive initial value leads to a solution which initially changes sign, but then becomes - and stays - positive again for sufficiently large…

A natural example of evolution can be described by a time-dependent two degrees-of-freedom Hamiltonian. We choose the case where initially the Hamiltonian derives from a general cubic potential, the linearised system has frequencies 1 and…

We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial…

We obtain slow dynamics for self-adjoint semigroups and unitary evolution groups. For semigroups, the slow dynamics is for orbits, and for the average return probability in the case of unitary evolution groups. We present an application to…

The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…

The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework…

This paper explores a non-linear, non-local model describing the evolution of a single species. We investigate scenarios where the spatial domain is either an arbitrary bounded and open subset of the $n$-dimensional Euclidean space or a…

In the paper we consider the linear inverse problem that consists in recovering the initial state in a first order evolution equation generated by a skew-adjoint operator. We studied the well-posedness of the inversion in terms of the…

Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…

We study linearization models for continuous one-parameter semigroups of parabolic type. In particular, we introduce new limit schemes to obtain solutions of Abel's functional equation and to study asymptotic behavior of such semigroups.…

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…

We obtain a lower bound for the period of periodic solutions of semilinear evolution equations for the full range of nonlinear terms for which standard local existence theory applies. This lower bound depends on the Lipschitz constant of…

We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…

We investigate slowly converging solutions for non-linear evolution equations of elliptic or parabolic type. These equations arise from the study of isolated singularities in geometric variational problems. Slowly converging solutions have…

It is well known that, in the study of the dynamical properties of nonlinear evolution system with nonlocal dispersals, the principal eigenvalue of linearized system play an important role. However, due to lack of compactness, in order to…

The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic…