Nonsmooth one-dimensional maps: some basic concepts and definitions
The main purpose of the present survey is to contribute to the theory of dynamical systems
defined by one-dimensional piecewise monotone maps. We recall some definitions known …
defined by one-dimensional piecewise monotone maps. We recall some definitions known …
Spinning black holes with axion hair
C Burrage, PGS Fernandes, R Brito… - Classical and Quantum …, 2023 - iopscience.iop.org
In this work we construct and analyze non-perturbative stationary and axially-symmetric
black hole solutions in general relativity coupled to an electromagnetic and an axion field …
black hole solutions in general relativity coupled to an electromagnetic and an axion field …
Revisiting the model of credit cycles with good and bad projects
We revisit the model of endogenous credit cycles by Matsuyama (2013, Sections 2–4). First,
we show that the same dynamical system that generates the equilibrium trajectory is …
we show that the same dynamical system that generates the equilibrium trajectory is …
Bifurcation sequences and multistability in a two-dimensional piecewise linear map
Bifurcation mechanisms in piecewise linear or piecewise smooth maps are quite different
with respect to those occurring in smooth maps, due to the role played by the borders. In this …
with respect to those occurring in smooth maps, due to the role played by the borders. In this …
Border collision bifurcations in a piecewise linear duopoly model
We consider a duopoly model characterized by a two-dimensional non-invertible continuous
map T given by piecewise linear functions, with several partitions, defining a duopoly game …
map T given by piecewise linear functions, with several partitions, defining a duopoly game …
2D discontinuous piecewise linear map: Emergence of fashion cycles
We consider a discrete-time version of the continuous-time fashion cycle model introduced
in Matsuyama, 1992. Its dynamics are defined by a 2D discontinuous piecewise linear map …
in Matsuyama, 1992. Its dynamics are defined by a 2D discontinuous piecewise linear map …
A robust route to randomness in a simple Cournot duopoly game where ambiguity aversion meets constant expectations
In this paper we investigate the dynamics of a duopoly game with ambiguity aversion
regarding uncertainty in demand and constant expectations concerning competitor …
regarding uncertainty in demand and constant expectations concerning competitor …
A financial market model with two discontinuities: Bifurcation structures in the chaotic domain
We continue the investigation of a one-dimensional piecewise linear map with two
discontinuity points. Such a map may arise from a simple asset-pricing model with …
discontinuity points. Such a map may arise from a simple asset-pricing model with …
Ambiguity aversion as a route to randomness in a duopoly game
The global dynamics is investigated for a duopoly game where the perfect foresight
hypothesis is relaxed and firms are worst-case maximizers. Overlooking the degree of …
hypothesis is relaxed and firms are worst-case maximizers. Overlooking the degree of …
The two-dimensional border-collision normal form with a zero determinant
DJW Simpson - arXiv preprint arXiv:2408.04790, 2024 - arxiv.org
The border-collision normal form is a piecewise-linear family of continuous maps that
describe the dynamics near border-collision bifurcations. Most prior studies assume each …
describe the dynamics near border-collision bifurcations. Most prior studies assume each …