We investigate population models with both continuous and discrete elements. Birth is assumed to occur at discrete instants of time whereas death and competition for resources and space occur continuously during the season. We compare the dynamics of such discrete-continuous hybrid models with the dynamics of purely discrete models where within-season mortality and competition are modelled dire...

The state spaces of machines admit the structure of time. A homotopy theory respecting this additional structure can detect machine behavior unseen by classical homotopy theory. In an attempt to bootstrap classical tools into the world of abstract spacetime, we identify criteria for classically homotopic, monotone maps of pospaces to future homotope, or homotope along homotopies monotone in bot...

We study continuous countably-piecewise monotone interval maps and formulate conditions under which these are conjugate to maps of constant slope, particularly when this slope is given by the topological entropy of the map. We confine our investigation to the Markov case and phrase our conditions in the terminology of the Vere-Jones classification of infinite matrices.

Introduction. It is well known that a nondegenerate continuum (compact, connected metric space) is chainable if and only if it is homeomorphic to the limit of an inverse sequence of arcs with bonding maps onto. Several authors have studied chainable continua as inverse limits of arcs and in particular Henderson [3] and Mahavier [4] have contributed to the problem of characterizing the class C o...

We consider a piecewise continuous, piecewise monotone interval map and a weight of bounded variation, constant on homtervals and continuous at periodic points of the map. With these data we associate a sequence of weighted Milnor-Thurston kneading matrices, converging to a countable matrix with coeecients analytic functions. We show that the determinants of these matrices converge to the inver...

In this note we consider a collection C of one parameter families of unimodal maps of [0, 1]. Each family in the collection has the form {μf} where μ ∈ [0, 1]. Denoting the kneading sequence of μf by K(μf), we will prove that for each member of C, the map μ 7→ K(μf) is monotone. It then follows that for each member of C the map μ 7→ h(μf) is monotone, where h(μf) is the topological entropy of μ...

Let L be a non empty relational structure. One can check that idL is monotone. Let S, T be non empty relational structures and let f be a map from S into T . Let us observe that f is antitone if and only if: (Def. 1) For all elements x, y of S such that x ¬ y holds f(x) ­ f(y). Next we state several propositions: (1) Let S, T be relational structures, K, L be non empty relational structures, f ...

The satisfiabil i ty problem for a syllogistic embracing 6, E, Boolean set operations, the Kuratowski topological closure operation ~~, and continuous and closed maps between topological spaces, along w i th the operations of point evaluation, set image, and inverse set image, is solved for formulae that meet a particular syntactic non-circulari ty property. The unquantif ied interpreted langua...

We study invariant measures of families of monotone twist maps Sγ(q, p) = (2q−p+γ ·V ′(q), q) with periodic Morse potential V . We prove that there exist a constant C = C(V ) such that the topological entropy satisfies htop(Sγ) ≥ log(C · γ)/3. In particular, htop(Sγ) → ∞ for |γ| → ∞. We show also that there exist arbitrary large γ such that Sγ has nonuniformly hyperbolic invariant measures μγ w...