Using methods from Convex Analysis, for each generalized pressure function we define an upper semi-continuous affine entropy-like map, establish abstract variational principle both countably and finitely additive probability measures prove that equilibrium states always exist. We show this conceptual approach imparts a new insight on dynamical systems without measure with maximal entropy, may b...

Let $\mathcal {M}$ be a $1$-cusped hyperbolic $3$-manifold whose cusp shape is quadratic. We show that there exists $c=c(\mathcal {M})$ such the number of Dehn fillings with any given volume $v$ uniformly bounded by $c$.

This study investigated bending, buckling, and free vibration responses of hyperbolic shear deformable functionally graded (FG) higher order beams. The material properties of FG beams are varied through thickness according to power law distribution; here, the FG beam was made of aluminium/alumina, and the hyperbolic shear deformation theory was used to evaluate the effect of shear deformation i...

We report the numerical observation of scarring, that is enhancement probability density around unstable periodic orbits a chaotic system, in eigenfunctions classical Perron-Frobenius operator noisy Anosov ("cat") maps, as well Bunimovich stadium. A parallel drawn between and quantum scars, based on unitarity or non-unitarity respective propagators. For uniformly hyperbolic systems such cat map...

We prove a strong version of quantum ergodicity for linear hyperbolic maps of the torus (“cat maps”). We show that there is a density one sequence of integers so that as N tends to infinity along this sequence, all eigenfunctions of the quantum propagator at inverse Planck constant N are uniformly distributed. A key step in the argument is to show that for a hyperbolic matrix in the modular gro...

For complex parameters a, c, we consider the Hénon mapping Ha,c : C → C, given by (x, y) 7→ (x + c−ay, x), and its Julia set, J . In this paper, we describe a rigorous computer program for attempting to construct a cone field in the tangent bundle over J , which is preserved by DH, and a continuous norm in which DH (and DH) uniformly expands the cones (and their complements). We show a conseque...

A fixed point theorem is proved for inverse transducers, leading to an automatatheoretic proof of the fixed point subgroup of an endomorphism of a finitely generated virtually free group being finitely generated. If the endomorphism is uniformly continuous for the hyperbolic metric, it is proved that the set of regular fixed points in the hyperbolic boundary has finitely many orbits under the a...

Consider a C 1+ diieomorphism f having a uniformly hyperbolic compact invariant set , maximal invariant in some small neighbourhood of itself. The asymp-totic exponential rate of escape from any small enough neighbourhood of is given by the topological pressure of ? log jJ u fj on (Bowen{Ruelle 1975]). It has been conjectured (Eckmann{Ruelle 1985]) that this property, formulated in terms of esc...