Related papers: Equilibrium States for Piecewise Weakly Convex Int…

We characterize weakly harmonic maps with respect to non-local Dirichlet forms by Markov processes and martingales. In particular, we can obtain discontinuous martingales on Riemannian manifolds from the image of symmetric stable processes…

In this paper we show that the classical results on the existence and uniqueness of moment maps in symplectic geometry generalize directly to weak homotopy moment maps in multisym- plectic geometry. In particular, we show that their…

Stability of nonconvex quadratic programming problems under finitely many convex quadratic constraints in Hilbert spaces is investigated. We present several stability properties of the global solution map, and the continuity of the optimal…

We establish some new common fixed point theorems of single-valued and multivalued mappings operating between complete ordered locally convex spaces under weaker assumptions. As an application, we prove a new minimax theorem of existence of…

Using the KKM technique, we establish some existence results for variational-hemivariational inequalities involving monotone set valued mappings on bounded, closed and convex subsets in reflexive Banach spaces. We also derive several…

Using the setting of $G$-metric spaces, common fixed point theorems for four maps satisfying the weakly commuting conditions are obtained for various generalized contractive conditions. Several examples are also presented to show the…

For a finitely irreducible countable Markov shift and a potential with summable variations, we provide a condition on the associated pressure function which ensures that Bowen's Gibbs state, the equilibrium state, and the minimizer of the…

We prove the existence and nonlinear stability of Camm type steady states of the Vlasov-Poisson system in the gravitational case. The paper demonstrates the effectiveness of an approach to the existence and stability problem for steady…

We prove uniqueness of equivariant harmonic maps into irreducible symmetric spaces of non-compact type and Euclidean buildings associated to isometric actions by Zariski dense subgroups.

In this work, based on Pinheiro for deterministic systems, we extend the notion of zooming systems to the random context and based on the technique of Arbieto-Matheus-Oliveira we prove the existence of equilibrium states for which we call…

Piecewise smooth systems are intensively studied today in many application areas, such as economics, finance, engineering, biology, and ecology. In this work, we consider a class of one-dimensional piecewise linear discontinuous maps with a…

We study inhomogeneous continuous-time weakly ergodic Markov chains with a finite state space. We introduce the notion of a Markov chain with the regular structure of an infinitesimal matrix and study the sharp upper bounds on the rate of…

We prove the existence of equilibrium states for partially hyperbolic endomorphisms with one-dimensional center bundle. We also prove, regarding a class of potentials, the uniqueness of such measures for endomorphisms defined on the 2-torus…

We show the existence of Lebesgue-equivalent conservative and ergodic $\sigma$-finite invariant measures for a wide class of one-dimensional random maps consisting of piecewise convex maps. We also estimate the size of invariant measures…

We study countably piecewise continuous, piecewise monotone interval maps. We establish a necessary and sufficient criterion for the existence of a nondecreasing semiconjugacy to a map of constant slope in terms of the existence of an…

This paper gives the definition of the Conley index for a piecewise continuous map, which is only well defined on compatible isolating neighborhoods with Wazewski property slightly weaker than continuous situation.

We develop the specification and orbit-decomposition approach to equilibrium states for parabolic rational maps of the Riemann Sphere. Our result extends the well-known results on uniqueness of equilibrium states in this setting, notably…

We study the rate of decay of correlations for equilibrium states associated to a robust class of non-uniformly expanding maps where no Markov assumption is required. We show that the Ruelle-Perron-Frobenius operator acting on the space of…

Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of…

First, a new sufficient condition for uniqueness of weak solutions is proved for the system of 2D viscous Primitive Equations. Second, global existence and uniqueness are established for several classes of weak solutions with partial…