Related papers: Star fows and multisingular hyperbolicity
We define a new version of modified mean curvature flow (MMCF) in hyperbolic space $\mathbb{H}^{n+1}$, which interestingly turns out to be the natural negative $L^2$-gradient flow of the energy functional defined by De Silva and Spruck in…
We prove that for generic three-dimensional vector fields, domination implies singular hyperbolicity.
We prove that oriented and standard shadowing properties are equivalent for topological flows on closed surfaces with the nonwandering set consisting of the finite number of critical elements (i.e., singularities or closed orbits).…
I address the following issues: All bulk velocity measurements (but one) are consistent with our standard gravitational instability theory. New accurate data and reconstruction methods allow high-resolution dynamical analysis nearby,…
The Hodge star mean curvature flow on a 3-dimensional Riemannian or pseudo-Riemannian manifold is a natural nonlinear dispersive curve flow in geometric analysis. A curve flow is integrable if the local differential invariants of a solution…
Let M be a smooth closed manifold and T*M its cotangent bundle endowed with the usual symplectic structure. A hypersurface S in T*M is said to be fiberwise starshaped if for each point q in M the intersection of S with the fiber at q is…
Hamiltonian flows on compact surfaces are characterized, and the topological invariants of such flows with finitely many singular points are constructed from the viewpoints of integrable systems, fluid mechanics, and dynamical systems.…
Star complexes are the highest level groupings in the hierarchy of the embedded young stars, clusters and associations, which obey the size - age relation. Starburst clumps, superassociations, supergiant HII regions are different titles for…
In this review, we discuss whether the present solar dynamo models can be extrapolated to explain various aspects of stellar activity. We begin with a summary of the following kinds of data for solar-like stars: (i) data pertaining to…
Most numerical models of binary stars - in particular neutron stars in compact binaries - assume the companions to be either corotational or irrotational. Either one of these assumptions leads to a significant simplification in the…
Every volume-preserving centre-bunched fibred partially hyperbolic system with 2-dimensional centre either (1) has two distinct centre Lyapunov exponents, or (2) exhibits an invariant continuous line field (or pair of line fields) tangent…
A set is star-shaped if there is a point in the set that can see every other point in the set in the sense that the line-segment connecting the points lies within the set. We show that testing whether a non-empty compact smooth region is…
A distribution of rank $4$ on a $7$-dimensional manifold is called a $(4, 7)$-distribution if its local sections generate the whole tangent space by taking Lie brackets once. Singular curves of $(4, 7)$-distributions are studied in this…
Recently many people have discussed the possibility that the universe is hyperbolic and was in an inflationary phase in the early stage. Under these assumptions, it is shown that the universe cannot have compact hyperbolic time-slices.…
An isolated massive star can blow a bubble, while a group of massive stars can blow superbubbles. In this paper, we examine three intriguing questions regarding bubbles and superbubbles: (1) why don't we see interstellar bubbles around…
Based on the large number of elliptical planetary nebulae I argue that about 55 per cent of all progenitors of planetary nebulae have planets around them. The planets spin up the stars when the later evolve along the red giant branch or…
Like the solar cycle, stellar activity cycles are also irregular. Observations reveal that rapidly rotating (young) Sun-like stars exhibit a high level of activity with no Maunder-like grand minima and rarely display smooth regular activity…
The well known stability conjecture of Palis and Smale states that if a diffeomorphism is structurally stable then the chain recurrent set is hyperbolic. It is natural to ask if this type of results is true for an individual chain class,…
We discuss the observed multiplicity of massive stars and implications on theories of massive star formation. After a short summary of the literature on massive star multiplicity, we focus on the O- and B-type stars in the Orion Nebula…
We consider a star as a compressible fluid subject to gravitational and magnetic forces. This leads to an Euler-Poisson system coupled to a magnetic field, which may be regarded as an MHD model together with gravity. The star executes…