相关论文: On the integrability of the n-centre problem
We consider a restricted $(N+1)$-body problem, with $N \geq 3$ and homogeneous potentials of degree $-\a<0$, $\a \in [1,2)$. We prove the existence of infinitely many collision-free periodic solutions with negative and small Jacobi constant…
In this note, we show that there exists an autoequivalence of positive categorical entropy on the derived category of bielliptic surfaces. This gives the first example of a surface admitting positive categorical entropy in the absence of…
We prove several general results on non existence of analytic first integrals for analytic diffeomorphisms possessing a hyperbolic fixed point.
We study the topological entropy of the Lagrangian flow restricted to an energy level $E_{L}^{-1}(c) \subset TM$ for $ c >e_0(L)$. We prove that if the flow of the Tonelli Lagrangian $ L: M \to \mathbb{R}$, on a closed manifold of dimension…
When a real fluid is expelled quickly from a tube, it forms a jet separated from the surrounding fluid by a thin, turbulent layer. On the other hand, when the same fluid is sucked into the tube, it comes in from all directions, forming a…
This paper considers a family of non-diffusive active scalar equations where a viscosity type parameter enters the equations via the constitutive law that relates the drift velocity with the scalar field. The resulting operator is smooth…
Over the past decades, research on two-dimensional melting has established that both first-order and continuous hexatic-liquid transitions can occur, influenced by various factors in the potential energy and system details. The fundamental…
It has been recently proposed that the interpretation of gravity as an emergent, entropic force might have nontrivial implications to cosmology. Here two approaches are investigated: in one, the Friedman equation receives entropic…
An example of a real-analytic metric on a compact manifold whose geodesic flow is Liouville integrable by $C^\infty$ functions and has positive topological entropy is constructed.
We discuss a large class of conformally invariant curvature energies for immersed hypersurfaces of dimension 4. The class under study includes various examples that have appeared in the recent literature and which arise from different…
We study a class of singular dynamical systems which generalise the classical N-centre problem of Celestial Mechanics to the case in which the configuration space is a Riemannian surface. We investigate the existence of topological…
On the basis of the balance equations for energy-momentum, spin, particle and entropy density, an approach is considered which represents a comparatively general framework for special- and general-relativistic continuum thermodynamics. In…
It is shown that the entropy of systems with large number of degrees of freedom is practically independent of observers, contrary to the claim of hep-th/0310022.
The energy-influx/entropy-influx relation in the Green-Naghdi Type III theory of heat conduction is examined within a thermodynamical framework \`a la Mueller-Liu, where that relation is not specified a priori irrespectively of the…
We investigate a class of parametric elliptic eigenvalue problems with homogeneous essential boundary conditions where the coefficients (and hence the solution $u$) may depend on a parameter $y$. For the efficient approximate evaluation of…
Recently the formation of an expanding universe from the (1+3+6)-dimensional space-times has been proposed on the basis of super-string theory. The serious entropy problem must be solved for it to be realistic from the cosmological…
We present a pedagogical review of old inconsistencies of Classical Electrodynamics and of some new ideas that solve them. Problems with the electron equation of motion and with the non-integrable singularity of its self-field energy tensor…
Compressible (full) potential flow is expressed as an equivalent first-order system of conservation laws for density $\rho$ and velocity $v$. Energy $E$ is shown to be the only nontrivial entropy for that system in multiple space…
Exact calculations are given for the Casimir energy for various fields in $R\times S^3$ geometry. The Green's function method naturally gives a result in a form convenient in the high-temperature limit, while the statistical mechanical…
We construct Z^2-SFTs at every computable level of the hierarchy of topological completely positive entropy (TCPE), answering Barbieri and Garc\'{i}a-Ramos, who asked if there was one at level 3. Furthermore, we show the property of TCPE in…