相关论文: Local perturbations of conservative $C^1$-diffeomo…
In this paper, we study deformations of coisotropic submanifolds in a locally conformal symplectic manifold. Firstly, we derive the equation that governs $C^\infty$ deformations of coisotropic submanifolds and define the corresponding…
In quantum theory, observables with a continuous spectrum are known to be fundamentally different from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for…
We show examples which reveal influences of spatial topologies to dynamics, using a class of spatially {\it closed} inhomogeneous cosmological models. The models, called the {\it locally U(1)$\times$U(1) symmetric models} (or the {\it…
An analytical method for investigation of the evolution of dynamical systems {\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application…
New one-leg multistep time discretizations of nonlinear evolution equations are investigated. The main features of the scheme are the preservation of the nonnegativity and the entropy-dissipation structure of the diffusive equations. The…
We study $C^1$-robustly transitive and nonhyperbolic diffeomorphisms having a partially hyperbolic splitting with one-dimensional central bundle whose strong un-/stable foliations are both minimal. {In dimension $3$, an important class of…
The Nielsen-Thurston theory of surface diffeomorphisms shows that useful dynamical information can be obtained about a surface diffeomorphism from a finite collection of periodic orbits.In this paper, we extend these results to homoclinic…
Conservation and consistency are fundamental properties of discretizations of systems of hyperbolic conservation laws. Here, these concepts are extended to the realm of iterative methods by formally defining locally conservative and flux…
Recent advances in levitated optomechanics provide new perspectives for the use of rotational degrees of freedom for the development of quantum technologies as well as for testing fundamental physics. As for the translational case, their…
The rotation induced inhomogeneous problem is non-trivial and inevitable. In this paper a generic framework is developed to investigate the inhomogeneous condensate in a system of fermions under the presence of rotation. It is a…
We present a new class of exponential integrators for ordinary differential equations: locally exact modifications of known numerical schemes. Local exactness means that they preserve the linearization of the original system at every point.…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
Eccentric Keplerian discs are believed to be unstable to three-dimensional hydrodynamical instabilities driven by the time-dependence of fluid properties around an orbit. These instabilities could lead to small-scale turbulence, and…
We show that C^r generically in the space of C^r conservative diffeomorphisms of a compact surface, every hyperbolic periodic point has a transverse homoclinic orbit
Contrary to the established view of the Lorenz system as an archetype of dissipative chaos lacking conserved quantities, this work rigorously demonstrates the existence of a novel class of history-dependent dynamical invariants. Through a…
This work explores the dynamic properties of test particles surrounding a distorted, deformed compact object. The astrophysical motivation was to choose such background, which could constitute a more reasonable model of a real situation…
We present a structure-preserving discretization of the hybrid magnetohydrodynamics (MHD)-driftkinetic system for simulations of low-frequency wave-particle interactions. The model equations are derived from a variational principle,…
Franson showed that Aspect's experiment to test Bell's inequality did not rule out local realistic theories with delayed determinism. A class of local, deterministic discrete mathematical models with delayed determinism is described that…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
We present reduction and reconstruction procedures for the solutions of symmetric stochastic differential equations, similar to those available for ordinary differential equations. Additionally, we use the local tangent-normal…