Related papers: Contact mappings of differential equations
An orientation preserving diffeomorphism over a surface embedded in a 4-manifold is called extendable, if this diffeomorphism is a restriction of an orientation preserving diffeomorphism on this 4-manifold. In this paper, we investigate…
We consider the evolution of correlation functions in a non-Markov version of the contact model in the continuum. The memory effects are introduced by assuming the fractional evolution equation for the statistical dynamics. This leads to a…
Modified Hamiltonians are used in the field of geometric numerical integration to show that symplectic schemes for Hamiltonian systems are accurate over long times. For nonlinear systems the series defining the modified Hamiltonian usually…
We solve a problem on a construction of a separately continuous mapping with the given diagonal, which is the pointwise limit of a sequence of continuous mappings valued in an equiconnected space. We construct an example of a closed-valued…
The theory of polynomial-like maps is of fundamental importance in holomorphic dynamics. We study dynamical properties of a larger class of maps. Our main result is that, under some natural conditions, a map of this class has a completely…
We study bifurcations of non-orientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on non-orientable two-dimensional surfaces. We consider one and two parameter general unfoldings…
Connections between Lie derivatives and the deviation equation has been investigated in spaces with affine connection. The deviation equations of the geodesics as well as deviation equations of non-geodesics trajectories have been obtained…
The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the…
Let $T$ be a competitive map on a rectangular region $\mathcal{R}\subset \mathbb{R}^2$, and assume $T$ is $C^1$ in a neighborhood of a fixed point $\bar{\rm x}\in \mathcal{R}$. The main results of this paper give conditions on $T$ that…
This work further develops the properties of fractional differential forms. In particular, finite dimensional subspaces of fractional form spaces are considered. An inner product, Hodge dual, and covariant derivative are defined. Coordinate…
We exploit the Cartan-K\"ahler theory to prove the local existence of real analytic quaternionic contact structures for any prescribed values of the respective curvature functions and their covariant derivatives at a given point on a…
It is proved that the members of the Riccati hierarchy, the so-called Riccati chain equations, can be considered as particular cases of projective Riccati equations, which greatly simplifies the study of the Riccati hierarchy. This also…
We prove that the moduli space of contact stable maps to $\mathbb{P}^{2n+1}$ of degree $d$ admits a stratification parameterized by graphs. We use it to determine the number of irreducible rational contact curves in $\mathbb{P}^{2n+1}$ with…
Systems of partial differential equations which appear in classical field theories can be studied geometrically using different geometrical structures, for example, k-symplectic geometry, k-cosymplectic geometry, multisymplectic geometry,…
The one-dimensional shallow water equations in Eulerian coordinates are considered. Relations between symmetries and conservation laws for the potential form of the equations, and symmetries and conservation laws in Eulerian coordinates are…
A long-standing question is what invariant sets can be shared by two maps acting on the same space. A similar question stands for invariant measures. A particular interesting case are expanding Markov maps of the circle. If the two involved…
In this paper, we introduce restricted products for families of locally convex spaces and formulate criteria ensuring that mappings into such products are continuous or smooth. As a special case, can define restricted products of weighted…
In this paper, we develop an algebraic approach to classifying contact symmetries of the second-order nonlinear evolution equations. Up to contact isomorphisms, all inequivalent PDEs admitting semi-simple algebras, solvable algebras of…
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…
A new characterization is provided for the class of compact rank-one symmetric spaces. Such spaces are the only symmetric spaces of compact type for which the standard vector field on their sphere bundles is Killing with respect to some…