Related papers: A hyperbolic analog of the phasor addition formula

Quantum and classical mechanics share a common algebraic formalism which is expressed naturally in the language of category theory. A third realization of this formalism is the so-called hyperbolic quantum mechanics where split-complex…

In this paper, we try to give the appropriate class of languages to which belong various objects associated with tessellations in the hyperbolic plane.

We study a class of two dimensional partially hyperbolic systems, not necessarily skew products, trying to establish the germ of a general theory. To illustrate the scope of the theory, we apply our results to the case of fast-slow…

We construct the Hamiltonian formalism of bigravity for the potential of a general form. We find conditions on this potential and prove that under these conditions the formalism is equivalent to the one constructed with the celebrated…

In this paper, the versions of trigonometric functions of certain known inequalities for hyperbolic ones are proved, and then corresponding inequalities for means are presented.

In this paper it is proved that relative hyperbolicity is an invariant of quasi-isometry. As a byproduct of the arguments, simplified definitions of relative hyperbolicity are obtained. In particular we obtain a new definition very similar…

We give necessary and sufficient conditions for a hyperbolic set to be non-chaotic (or, conversely, chaotic) in a certain sense.

We introduce measure-theoretic definitions of {\it hyperbolic structure for measure-preserving automorphisms}. A wide class of $K$-automorphisms possesses a hyperbolic structure; we prove that all $K$-automorphisms have a slightly weaker…

In this study we give the hyperbolic version of classical Menelaus theorem for quadrilaterals.

This article gives a conceptual introduction to the topos approach to the formulation of physical theories.

In order to discuss the well-posed initial value formulation of the teleparallel gravity and apply it to numerical relativity a symmetric hyperbolic system in the self-dual teleparallel gravity which is equivalent to the Ashtekar…

In this paper we continue the study of non-diagonalisable hyperbolic systems with variable multiplicity started by the authors in \cite{Garetto2018}. In the case of space dependent coefficients, we prove a representation formula for…

There is a wealth of results in the literature on the thermodynamic formalism for potentials that are, in some sense, "hyperbolic". We show that for a sufficiently regular one-dimensional map satisfying a weak hyperbolicity assumption,…

By means of the contour integration method, we evaluate, in closed form, a class of definite integrals involving hyperbolic tangent function.

This paper proposes a basic theory on physical reality and a new foundation for quantum mechanics and classical mechanics. It presents a scenario not only to solve the problem of the arbitrariness on the operator ordering for the…

We study partially hyperbolic diffeomorphisms satisfying a trapping property which makes them look as if they were Anosov at large scale. We show that, as expected, they share several properties with Anosov diffeomorphisms. We construct an…

We provide hyperbolic analogues of some classical theorems in spherical geometry due to Menelaus, Euler, Lexell, Ceva and Lambert. Some of the spherical results are also made more precise.

We establish pointwise ergodic theorems for a large class of natural averages on simple Lie groups of real-rank-one, going well beyond the radial case considered previously. The proof is based on a new approach to pointwise ergodic…

In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can…

Taking quantum formalism as a point of reference and connection, we explore the various possibilities that arise in the construction of physical theories. Analyzing the distinct physical phenomena that each of them may describe, we…