Related papers: A note on an open conjecture in rational dynamical…
We survey Vojta's higher-dimensional generalizations of the $abc$ conjecture and Szpiro's conjecture as well as recent developments that apply them to various problems in arithmetic dynamics. In particular, the "$abcd$ conjecture" implies a…
A new master equation to mimic the dynamics of a collection of interacting random walkers in an open system is proposed and solved numerically.In this model, the random walkers interact through excluded volume interaction (single-file…
In dynamic settings each economic agent's choices can be revealing of her private information. This elicitation via the rationalization of observable behavior depends each agent's perception of which payoff-relevant contingencies other…
For a real number $0<\lambda<2$, we introduce a transformation $T_\lambda$ naturally associated to expansion in $\lambda$-continued fraction, for which we also give a geometrical interpretation. The symbolic coding of the orbits of…
The novel proposal to invoke the split of the Ricci scalar into bulk and boundary terms in the gravitational action, opens up a new avenue of investigation into stellar dynamics. The Lagrangian contains functional forms of the bulk term…
The dynamics of a closed quantum system, under a unitary time evolution $U$, is, obviously, linear. But, the reduced dynamics of an open quantum system $S$, interacting with an environment $E$, is not linear, in general. Dominy et al.…
The dynamics of the second order rational difference equation $\displaystyle{z_{n+1}=\frac{\alpha + \alpha z_{n}+\beta z_{n-1}}{1+z_{n}}}$ with complex parameters $\alpha$, $\beta$ and arbitrary complex initial conditions is investigated.…
The thesis of this paper is that truth-relevant logic is a better foundation for mathematics than classical logic. It is a system proposed by Richard Diaz in 1981. In a certain sense t-relevant logic is based on Kleene strong tables. These…
We investigate random complex dynamics of rational or polynomial maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, generically, the chaos of the averaged system disappears at any point in the Riemann…
We establish a flexible generalization of inductive systems of operator systems, which relaxes the usual transitivity (or coherence) condition to an asymptotic version thereof and allows for systems indexed over arbitrary nets. To…
The paper discusses the basic paradoxes of thermodynamics and quantum mechanics. The approaches to solution of these paradoxes are suggested. The first one relies on the influence of the external observer (environment), which disrupts the…
A new computational method that uses polynomial equations and dynamical systems to evaluate logical propositions is introduced and applied to Goedel's incompleteness theorems. The truth value of a logical formula subject to a set of axioms…
We address two mathematical aspects of the Bir\'o--N\'eda dynamical model, recently applied in the statistical analysis of several and varied complex phenomena. First, we show that a given implicit assumption ceases to be valid outside the…
In his Comment [1], Philip Strasberg (PS) argues from the analysis of different examples that the framework we have presented in [2] does not recover known results of macroscopic textbook thermodynamics. Here, we show that such apparent…
This paper deals with the long-term behavior of positive solutions for the following parabolic-elliptic chemotaxis competition system with weak singular sensitivity and logistic source \begin{equation} \label{abstract-eq} \begin{cases}…
It was recently conjectured that every component of a discrete-time rational dynamical system is a solution to an algebraic difference equation that is linear in its highest-shift term (a quasi-linear equation). We prove that the conjecture…
We study the following system of two rational difference equations x_n=({\beta}_k x_(n-k)+{\gamma}_k y_(n-k))/(A+\Sigma_(j=1)^l[B_j x_(n-j) ]+\Sigma_(j=1)^l[C_j y_(n-j) ]), n \in N, y_n=({\delta}_k x_(n-k)+\in_k…
Boolean automata networks, genetic regulation networks, and metabolic networks are just a few examples of biological modelling by discrete dynamical systems (DDS). A major issue in modelling is the verification of the model against the…
A consistent set of six integrable discrete and continuous dynamical systems are suggested corresponding to arbitrary affine Lie algebra. The set contains a system of partial differential equations which can be treated as a version of…
The thermodynamic formalism expresses chaotic properties of dynamical systems in terms of the Ruelle pressure $\psi(\beta)$. The inverse-temperature like variable $\beta$ allows one to scan the structure of the probability distribution in…