Related papers: Symmetry Conserving Dynamical Mappings
A family of discontinuous symplectic maps on the cylinder is considered. This family arises naturally in the study of nonsmooth Hamiltonian dynamics and in switched Hamiltonian systems. The transformation depends on two parameters and is a…
Given a code from a shift space to an irreducible sofic shift, any two of the following three conditions -- open, constant-to-one, (right or left) closing -- imply the third. If the range is not sofic, then the same result holds when…
Special bases of orthogonal polynomials are defined, that are suited to expansions of density and potential perturbations under strict particle number conservation. Particle-hole expansions of the density response to an arbitrary…
Any symmetry reduces a second-order differential equation to a first-order equation: variational symmetries of the action (exemplified by central field dynamics) lead to conservation laws, but symmetries of only the equations of motion…
Iterations of odd piecewise continuous maps with two discontinuities, i.e., symmetric discontinuous bimodal maps, are studied. Symbolic dynamics is introduced. The tools of kneading theory are used to study the homology of the discrete…
This paper initiates a systematic development of a theory of non-commutative optimization. It aims to unify and generalize a growing body of work from the past few years which developed and analyzed algorithms for natural geodesically…
A (discrete) dynamical system may have various symmetries and reversing symmetries, which together form its so-called reversing symmetry group. We study the set of 3D trace maps (obtained from two-letter substitution rules) which preserve…
In this article we investigate the question which local symmetry preserving operations can not only preserve, but also increase the symmetry of a polyhedral map. Often operations that can increase symmetry, can nevertheless not do so for…
Discrete symmetries of dynamical flows give rise to relations between periodic orbits, reduce the dynamics to a fundamental domain, and lead to factorizations of zeta functions. These factorizations in turn reduce the labor and improve the…
This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general…
Motivated by the symmetry in the non-relativistic limit of anti-de Sitter geometry, we employ planar dynamical models featuring exotic (deformed) harmonic oscillators, presented through direct and indirect Lagrangian representations. The…
For the dynamics of a discontinuous map on a compact metric space, we describe an approach using suitable closed relations and connect it with the continuous dynamics on an invariant G-delta subset and with the continuous dynamics on the…
This work develops novel strategies for optimal planning with semantic observations using continuous state partially observable markov decision processes (CPOMDPs). Two major innovations are presented in relation to Gaussian mixture (GM)…
In this paper we describe a 1-dimensional variational approach to the analytical construction of equivariant biharmonic maps. Our goal is to provide a direct method which enables analysts to compute directly the analytical conditions which…
Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the…
This paper presents an overview of physical ideas and mathematical methods for implementing non-smooth and discontinuous substitutions in dynamical systems. General purpose of such substitutions is to bring the differential equations of…
A geometric approach to integrability and reduction of dynamical system is developed from a modern perspective. The main ingredients in such analysis are the infinitesimal symmetries and the tensor fields that are invariant under the given…
We propose new algorithms for numerical integration of the equations of motion for classical spin systems with fixed spatial site positions. The algorithms are derived on the basis of a mid-point scheme in conjunction with the multiple time…
Resent works of Hawking and Susskind suggested that information is conserved in the universe. We extend this thesis and propose that dynamics of information - computations can conserve in Anti-de-Sitter cosmological model. Information…
We formulate a geometric measurement theory of dynamical classical systems possessing both continuous and discrete degrees of freedom. The approach is covariant with respect to choices of clocks and canonically incorporates laboratories.…