Related papers: The Dynamics of Twisted Tent Maps
The problem of planning for a robot that operates in environments containing a large number of objects, taking actions to move itself through the world as well as to change the state of the objects, is known as task and motion planning…
The iteration of rational maps is well-understood in dimension 1 but less so in higher dimensions. We study some maps on spaces of matrices which present a weak complexity with respect to the ring structure. First we give some properties of…
Given a graph and a representation of its fundamental group, there is a naturally associated twisted adjacency operator. The main result of this article is the fact that these operators behave in a controlled way under graph covering maps.…
Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and…
We compute the stable cohomology groups of the mapping class groups of compact orientable surfaces with one boundary, with twisted coefficients given by the homology of the unit tangent bundle of the surface. This stable twisted cohomology…
Due to their complexity, foliated structure problems often pose intricate challenges to task and motion planning in robotics manipulation. To counter this, our study presents the ``Foliated Repetition Roadmap.'' This roadmap assists task…
The twisted graph $T_{n}$ is a drawing of the complete graph with $n$ vertices $v_{1},v_{2},\ldots ,v_{n}$ in which two edges $v_{i}v_{j}$ ($i<j$) and $v_{s}v_{t}$ ($s<t$) cross if and only if $i<s<t<j$ or $s<i<j<t$. We show that for any…
We propose a new model of one-dimensional traffic flow using a coupled map lattice. In the model, each vehicle is assigned a map and changes its velocity according to it. A single map is designed so as to represent the motion of a vehicle…
Map generalization is a process of producing maps at different levels of detail by retaining essential properties of the underlying geographic space. In this paper, we explore how the map generalization process can be guided by the…
A stratified space is a kind of topological space together with a partition into smooth manifolds. These kinds of spaces naturally arise in the study of singular algebraic varieties, symplectic reduction, and differentiable stacks. In this…
In this PhD thesis we develop the frame work of triple crossing diagram maps (TCD maps), which describes constrained configurations of points in projective spaces and discrete dynamics on these configurations. We are able to capture the…
A mechanism for the localization of spatially periodic, self-organized patterns in anisotropic media which requires systems extended in all three spatial dimensions is presented: When the anisotropy axis is twisted the pattern becomes…
The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…
Recently, the theory concerning piecewise smooth vector fields (PSVFs for short) have been undergoing important improvements. In fact, many results obtained do not have an analogous for smooth vector fields. For example, the chaoticity of…
We consider a model of fragmentation of sheet by cracks that move with a velocity in preferred direction, but undergo random transverse displacements as they move. There is a non-zero probability of crack-splitting, and the split cracks…
Let $A$ be either a simplicial complex $K$ or a small category $\mathcal C$ with $V(A)$ as its set of vertices or objects. We define a twisted structure on $A$ with coefficients in a simplicial group $G$ as a function $$ \delta\colon…
A map which is non-orientable or has non-empty boundary has a canonical double cover which is orientable and has empty boundary. The map is called stable if every automorphism of this cover is a lift of an automorphism of the map. This note…
A (closed) dynamical system is a notion of how things can be, together with a notion of how they may change given how they are. The idea and mathematics of closed dynamical systems has proven incredibly useful in those sciences that can…
This paper is a step towards a systematic theory of the transitivity (clustering) phenomenon in random networks. A static framework is used, with adjacency matrix playing the role of the dynamical variable. Hence, our model is a matrix…
A method to define the complex structure and separate the conformal mode is proposed for a surface constructed by two-dimensional dynamical triangulation. Applications are made for surfaces coupled to matter fields such as $n$ scalar fields…