Related papers: Every period annulus is both reversible and symmet…

In this work we study the local structure of analytic planar vector fields that are reversible with respect to the linear involution $R(u,v)=(u,-v)$. We show that every analytic reversible vector field with a nondegenerate equilibrium is…

All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…

We show that every homomorphism from the infinite-dimensional unitary or orthogonal group to a separable group is continuous.

We split the generic conformal mechanical system into a "radial" and an "angular" part, where the latter is defined as the Hamiltonian system on the orbit of the conformal group, with the Casimir function in the role of the Hamiltonian. We…

Our purpose in this paper is to study when a planar differential system polynomial in one variable linearizes in the sense that it has an inverse integrating factor which can be constructed by means of the solutions of linear differential…

Here, I discuss some implications of the time-reversal invariance of lossless radiating systems. I highlight that time-reversal symmetry provides a rather intuitive explanation for the conditions of polarization and impedance matching of a…

The issue of irreversibility in a universe with time-reversal-symmetric laws is a central problem in physics. % , and, in particular, to statistical mechanics, information theory and quantum thermodynamics. In this letter, we discuss for…

Irreversibility and acausality of a sub-system are established in exactly soluble harmonic models with reversible and causal dynamics. It is shown that initial conditions, imposed on some dynamical degrees of freedom may break time reversal…

Let W be a weight-homogeneous planar polynomial differential system with a center. We find an upper bound of the number of limit cycles which bifurcate from the period annulus of W under a generic polynomial perturbation. We apply this…

We show that if $X$ is an arc-like continuum which can be represented as an inverse limit of a simplicial inverse system on arcs, then for every point $x \in X$ there is a plane embedding of $X$ in which $x$ is accessible. This answers a…

We close the problem of the existence of period annuli in planar piecewise linear differential systems with a straight line of nonsmoothness. In fact, a characterization for the existence of such objects is provided by means of a few basic…

The dilation method is a practical way to experimentally simulate non-Hermitian, especially $\cal PT$-symmetric quantum systems. However, the time-dependent dilation problem cannot be explicitly solved in general. In this paper, we present…

An element of a group is \emph{reversible} if it is conjugate to its own inverse, and it is \emph{strongly reversible} if it is conjugate to its inverse by an involution. A group element is strongly reversible if and only if it can be…

The evolution of any factorized time-reversible symplectic integrators, when applied to the harmonic oscillator, can be exactly solved in a closed form. The resulting modified Hamiltonians demonstrate the convergence of the Lie series…

We prove a separable reduction theorem for sigma-porosity of Suslin sets. In particular, if A is a Suslin subset in a Banach space X, then each separable subspace of X can be enlarged to a separable subspace V such that A is sigma-porous in…

Here we prove that a commuting variety associated with a symmetric pair (g, g_0) is irreducible for (so_{n+m}, so_n + so_m) and reducible for (gl_{n+m}, {gl}_n + gl_m) with n>m, (so_{2n}, gl_n) with odd n, (E_6, {so}_{10} + k).

In this paper we prove the non-isochronicity of $\Sigma$-centers for a class of planar piecewise smooth differential systems with a straight switching line, whose two sub-systems are Hamiltonian differential systems with a non-degenerated…

We show that if any four distinct solutions of a rational difference equation are algebraically independent, then any number of distinct solutions to the equation are independent. A nontrivial variant of this result is given for autonomous…

Esnault asked whether every smooth complex projective variety with infinite fundamental group has a nonzero symmetric differential (a section of a symmetric power of the cotangent bundle). In a sense, this would mean that every variety with…

The rewriting system sigma is the set of rules propagating explicit substitutions in the lambda-calculus with explicit substitutions. In this note, we prove the undecidability of unification modulo sigma.