Related papers: Second problem of globalization in the theory of d…
Formula for the force field of Newtonian dynamical systems admitting the normal shift of hypersurfaces in Riemannian manifolds is considered. Problem of globalization for geometric structures associated with this formula is studied.
We consider a generalization of the notion of a natural mechanical system to the case of additional forces of gyroscopic type. Such forces appear, for example, as a result of global reduction of a natural system with symmetry. We study…
Two-dimensional case in the theory of dynamical systems admitting the normal shift differs crucially from multidimensional case. Features of two-dimensional case are gathered and studied in this thesis.
Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…
Theory of Newtonian dynamical systems admitting normal shift of hypersurfaces was first developed for the case of Riemannian manifolds. Recently it was generalized for manifolds geometric equipment of which is given by some regular…
Development of theory of dynamical systems admitting the normal shift in 1993-1999 is reviewed. Basics are given with complete proofs.
We study the globalization of partial actions on sets and topological spaces and of partial coactions on algebras by applying the general theory of globalization for geometric partial comodules, as previously developed by the authors. We…
It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian…
Newtonian dynamical systems accepting the normal shift on an arbitrary Riemannian manifold are considered. Partial differential equations forming the weak and additional normality conditions for them are reported.
Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…
The formalism of integrable mappings is applied to the problem of constructing hierarchies of $(1+2)$ dimensional integrable systems in the $(2|2)$ superspace. We find new supersymmetric integrable mappings and corresponding to them new…
Numerical simulations on Ising Spin Glasses show that spin glass transitions do not obey the usual universality rules which hold at canonical second order transitions. On the other hand the dynamics at the approach to the transition appear…
The problem of formation of generic structures in the Universe is addressed, whereby first the kinematics of inertial continua for coherent initial data is considered. The generalization to self--gravitating continua is outlined focused on…
Synchronization has received a lot of attention from the scientific community for systems evolving on static networks or higher-order structures, such as hypergraphs and simplicial complexes. In many relevant real world applications, the…
Resilience is a concept of rising interest in computer science and software engineering. For systems in which correctness w.r.t. a safety condition is unachievable, fast recovery is demanded. We investigate resilience problems of graph…
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
Class of Newtonian dynamical systems admitting normal blow-up of points in Riemannian manifolds is considered. Geometric interpretation for weak normality condition, which arose earlier in the theory of dynamical systems admitting the…
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…
Abundant second-order maximally conformally superintegrable Hamiltonian systems are re-examined, revealing their underlying natural Weyl structure and offering a clearer geometric context for the study of St\"ackel transformations (also…
There is strong expectation that cities, across time, culture and level of development, share much in common in terms of their form and function. Recently, attempts to formalize mathematically these expectations have led to the hypothesis…