Related papers: On the creation of conjugate points for thermostat…

Thermoelectric devices at the nanoscale offer promising routes for on-chip refrigeration and waste-heat recovery, yet most semiconductor-based implementations suffer from limited tunability and narrow operational ranges. We introduce a…

We exhibit a continuously varying family $F_\lambda$ of homeomorphisms of the sphere $S^2$, for which each $F_\lambda$ is a measurable pseudo-Anosov map. Measurable pseudo-Anosov maps are generalizations of Thurston's pseudo-Anosov maps,…

A simple deterministic and time reversal invariant type of thermostat is proposed to be used for computer simulations of classical systems. It acts on collisions with the walls of the container exclusively. It maps the incoming and outgoing…

We construct non-trapping asymptotically hyperbolic manifolds with boundary conjugate points but no interior conjugate points.

We determine the homeomorphism type of the space of smooth complete nonnegatively curved metrics on surfaces of positive Euler characteristic equipped with the topology of $C^\gamma$ uniform convergence on compact sets, when $\gamma$ is…

We propose an alternative formalism to simulate CMB temperature maps in $\Lambda$CDM universes with nontrivial spatial topologies. This formalism avoids the need to explicitly compute the eigenmodes of the Laplacian operator in the spatial…

We consider functions with isolated critical points on a closed surface. We prove that in a neighborhood of a critical point the function conjugates with Re$z^k$ for the some nonnegative integer k. The full topological invariant of such…

Let $f$ be a non-invertible irreducible Anosov map on $d$-torus. We show that if the stable bundle of $f$ is one-dimensional, then $f$ has the integrable unstable bundle, if and only if, every periodic point of $f$ admits the same Lyapunov…

Given a smooth Hermitian vector bundle $\mathcal{E}$ over a closed Riemannian manifold $(M,g)$, we study generic properties of unitary connections $\nabla^{\mathcal{E}}$ on the vector bundle $\mathcal{E}$. First of all, we show that twisted…

In this note we show that for the construction of differentiable conjugation, the assumption of the existence of smooth bump function is not necessary, and consequently the corresponding conjecture stated in the paper of W. Zhang, K. Lu and…

The field of algorithmic self-assembly is concerned with the computational and expressive power of nanoscale self-assembling molecular systems. In the well-studied cooperative, or temperature 2, abstract tile assembly model it is known that…

Let $M$ be a closed oriented $C^\infty$ manifold and $f$ a $C^\infty$ Anosov diffeomorphism on $M$. We show that if $M$ is the two torus $T^2$, then $f$ is conjugate to a hyperbolic automorphism of $T^2$, either by a $C^\infty$…

We prove that if f is an orientation-preserving homeomorphism of a closed orientable surface M whose singular set is totally disconnected, then f is topologically conjugate to a conformal transformation.

For a twist map $f$ of the annulus preserving the Lebesgue measure, we give sufficient conditions to assure the existence of a set of positive measure of points with non-zero asymptotic torsion. In particular, we deduce that every bounded…

We consider a sequences of symplectic twist maps corresponding to Frenkel Kontorova variational functional. For such a sequence without conjugate points we construct an invariant Lagrangian subbundle. Using the ideas by E.Hopf from…

We prove the Ingram Conjecture, i.e., we show that the inverse limit spaces of every two tent maps with different slopes in the interval [1, 2] are non-homeomorphic. Based on the structure obtained from the proof, we also show that every…

Let $(M,g)$ be a compact Riemannian surface without boundary, $W^{1,2}(M)$ be the usual Sobolev space, $J: W^{1,2}(M)\rightarrow \mathbb{R}$ be the functional defined by $$J(u)=\frac{1}{2}\int_M|\nabla u|^2dv_g+8\pi \int_M…

We demonstrate the existence of topological insulators in one dimension protected by mirror and time-reversal symmetries. They are characterized by a nontrivial $\mathbb{Z}_2$ topological invariant defined in terms of the "partial"…

Antiferromagnetic topological insulators harbor topological in-gap surface states protected by an anti-unitary $S$ symmetry, which is broken by the inevitable presence of domain walls. Whether an antiferromagnetic topological insulator with…

Each compact Riemannian manifold with no conjugate points admits a family of functions whose integrals vanish exactly when central Busemann functions split linearly. These functions vanish when all central Busemann functions are sub- or…