Related papers: Global transport in a nonautonomous standard map
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding…
We study the dynamics of planar diffeomorphisms having a unique fixed point that is a hyperbolic local saddle. We obtain sufficient conditions under which the fixed point is a global saddle. We also address the special case of…
Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as $\textit{geometric…
Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of…
Energy level statistics of quantized chaotic systems have been evaluated in the semiclassical limit via their periodic orbits using the Gutzwiller and related trace formulae. Here we evaluate a spectral statistic of chaotic 4-regular…
In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on the dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures…
In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…
We provide new examples of integrable rational maps in four dimensions with two rational invariants, which have unexpected geometric properties, as for example orbits confined to non algebraic varieties, and fall outside classes studied by…
Periodic orbit theory allows calculations of long time properties of chaotic systems from traces, dynamical zeta functions and spectral determinants of deterministic evolution operators, which are in turn evaluated in terms of periodic…
We propose a global constructibility analysis for a vehicle moving on a planar surface. Assuming that the vehicle follows a trajectory that can be uniquely identified by the sequence of control inputs and by some intermittent ranging…
Changes in environmental or system parameters often drive major biological transitions, including ecosystem collapse, disease outbreaks, and tumor development. Analyzing the stability of steady states in dynamical systems provides critical…
This paper discusses reduction by symmetries for autonomous and non-autonomous forced mechanical systems with inelastic collisions. In particular, we introduce the notion of generalized hybrid momentum map and hybrid constants of the motion…
In this article we introduce a new type of cyclic contraction mapping on a pair of subsets of a metric space with a graph and prove best proximity points results for the same. Also, we demonstrate that the number of such points is same with…
We perform a numerical analysis of the gravitational field of a global monopole coupled nonminimally to gravity, and find that, for some given nonminimal couplings (in constrast with the minimal coupling case), there is an attractive region…
We discuss a two-parameter family of maps that generalize piecewise linear, expanding maps of the circle. One parameter measures the effect of a non-linearity which bends the branches of the linear map. The second parameter rotates points…
In this article, we attempt to study the possible link between the dynamics of a circle map and the caustics of its iterations. The attention is on a geometrically defined off-center reflections, which, coincidentally, is also a…
Human mobility is investigated using a continuum approach that allows to calculate the probability to observe a trip to anyarbitrary region, and the fluxes between any two regions. The considered description offers a general and unified…
We statistically compare the relationships between frequencies of digits in continued fraction expansions of typical rational points in the unit interval and higher dimensional generalisations. This takes the form of a Large Deviation and…
We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…
The destruction of regular regions in two-dimensional, area-preserving maps is traditionally described in terms of the breakup of invariant curves and the persistence of transport barriers. Here, we investigate how this scenario changes…