In this note, we show a polynomial bound for the growth of the lap number of a piecewise monotone and piecewise continuous interval map with nitely many periodic points. We use Milnor and Thurston's kneading theory with the coordinates of Baladi and Ruelle, which are useful for extending the theory to the non continuous case. We say that f : 0; 1] ! 0; 1] is piecewise strictly monotone piecewis...

Let f : π → π be a homeomorphism of the plane π. We define open sets P , called pruning fronts after the work of Cvitanović [C], for which it is possible to construct an isotopy H : π × [0, 1] → π with open support contained in ⋃ n∈Z f(P ) such that H(·, 0) = f(·) and H(·, 1) = fP (·), where fP is a homeomorphism under which every point of P is wandering. Applying this construction with f being...

In this paper, we introduce general classes of generalized monotonicity and generalized convexity. For each type of (relatively) generalized monotone map, we establish a relationship to (relatively) generalized convex function. In this way, we obtain first-order characterizations for various (relatively) generalized convex functions. Our results extend/generalize similar result obtained in [3].

In this paper, we consider the monotone inclusion problem consisting of the sum of a continuous monotone map and a point-to-set maximal monotone operator with a separable two-block structure and introduce a framework of block-decomposition prox-type algorithms for solving it which allows for each one of the single-block proximal subproblems to be solved in an approximate sense. Moreover, by sho...

An example is given of an area-preserving monotone twist map such that a uniformly hyperbolic structure exists on the closure of its Birkhoff maximizing orbits. This note provides a rigorous example of an area preserving monotone twist map / with the property that Df\ s has a uniformly hyperbolic structure, where B denotes the closure of the Birkhoff maximizing orbits. As shown by Mather [8] an...

Extending the previous work of Monteiro and Pang (1998), this paper studies properties of fundamental maps that can be used to describe the central path of the monotone nonlinear complementarity problems over the cone of symmetric positive semidefinite matrices. Instead of focusing our attention on a specific map as was done in the approach of Monteiro and Pang (W98), this paper considers a gen...

This paper describes a mathematical theory of “co-design”, in which the objects of investigation are “design problems”, defined as tuples of “functionality space”, “implementation space”, and “resources space”, together with a feasibility relation. “Monotone” design problems are those for which functionality and resources are partially ordered and related by an order-preserving map. This condit...

We study a generic piecewise monotone map f : [0, 1] → [0, 1] with a particular type of entropy-carrying set X. We show under certain conditions that maps sufficiently C-close to f with more topological entropy have entropy-carrying sets containing X. New homoclinic orbits are created to every periodic point of X. 2000 Mathematics Subject Classification (MSC2000). 37E05, 37B40, 37Gxx

In this paper, we first characterize the continuity of a map in space $ \mathcal{C} = BC(\mathcal{H},\mathbb{R}^m) equipped with compact open topology. Then show that linear lattice and nonlocal dispersal equations generate uniformly continuous semigroups Banach \mathcal{B} supremum norm. Finally, illustrate how to prove nonlinear monotone semiflows respect

Determinantal point processes (DPPs) have recently been proposed as computationally efficient probabilistic models of diverse sets for a variety of applications, including document summarization, image search, and pose estimation. Many DPP inference operations, including normalization and sampling, are tractable; however, finding the most likely configuration (MAP), which is often required in p...