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Let M be a complete non-compact Riemannian manifold. For p ∈ (1,+∞), let Δp be the p-Laplace operator on M. One says that M is p-hyperbolic if there exists a Green function for Δp (see [Ho1,2]); oth...
In this paper, we derive the extended magnetohydrodynamic models based on the moment closure of the Vlasov-Maxwell equation. We adopt the Grad type moment expansion which was firstly proposed in [12...
We point out that the thermodynamic equilibrium is not an interior point of the hyperbolicity region of Grad’s 13-moment system. With a compact expansion of the phase density, which is compacter tha...
We prove that the hyperbolicity cones of elementary symmetric polynomials are spectrahedral, i.e., they are slices of the cone of positive semidefinite matrices. The proof uses the matrix--tree theore...
Abstract: Let H be an infinite dimensional separable Hilbert space, X a compact Hausdorff space and f : X \rightarrow X a homeomorphism which preserves a Borel ergodic measure which is positive on non...
Abstract: We prove that the complex of free factors of a free group of finite rank is hyperbolic.
Abstract: J. Mather characterized uniform hyperbolicity of a discrete dynamical system as equivalent to invertibility of an operator on the set of all sequences bounded in norm in the tangent bundle o...
Abstract: These are lecture notes of a course held at IMPA, Rio de Janiero, in september 2010: the purpose was to present recent results on Kobayashi hyperbolicity in complex geometry. Our ultimate go...
Abstract: T. Saito and M. Teragaito asked in their paper whether Berge knots of type VII, which can be situated on the fiber surface of the lefthand trefoil, are hyperbolic, and showed that some infin...
It is well known that for a > 4, the dynamical behaviors of the logistic map fa(x) = ax(1 − x) on the maximal invariant compact set are “simple”, which could be clearly explained by the theories...
We prove that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional c...
The goal of the present paper is three-fold. First is to clarify the connection between the dominant energy condition and hyperbolicity properties of Lagrangian field theories.
Maxwell’s equations are considered in metric-free form, with a local but otherwise arbitrary constitutive law. After splitting Maxwell’s equations into evolution equations and constraints, we derive t...
The goal of the present paper is three-fold. First is to clarify the connection between the dominant energy condition and hyperbolicity properties of Lagrangian field theories. Second is to provide fu...
For each k > 0 we find an explicit function fk such that the topology of S inside the ball BS(p, r) is ‘bounded’ by fk(r) for every complete Riemannian surface (compact or noncompact) S with K  W...

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