Results 1 to 10 of about 49 (48)
Dold sequences, periodic points, and dynamics
Bulletin of the London Mathematical Society, Volume 53, Issue 5, Page 1263-1298, October 2021., 2021 Abstract In this survey we describe how the so‐called Dold congruence arises in topology, and how it relates to periodic point counting in dynamical systems.
Jakub Byszewski +2 more
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On Iteration of Bijective Functions with Discontinuities
Annales Mathematicae Silesianae, 2020 We present three different types of bijective functions f : I → I on a compact interval I with finitely many discontinuities where certain iterates of these functions will be continuous.
Fripertinger Harald
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Annales Mathematicae Silesianae, 2020 The paper consists of two parts. At first, assuming that (Ω, A, P) is a probability space and (X, ϱ) is a complete and separable metric space with the σ-algebra of all its Borel subsets we consider the set c of all ⊗ 𝒜-measurable and contractive in ...
Baron Karol
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Generalization of the Harmonic Weighted Mean Via Pythagorean Invariance Identity and Application
Annales Mathematicae Silesianae, 2020 Under some simple conditions on the real functions f and g defined on an interval I ⊂ (0, ∞), the two-place functions Af (x, y) = f (x) + y − f (y) and Gg(x,y)=g(x)g(y)y{G_g}\left({x,y} \right) = {{g\left(x \right)} \over {g\left(y \right)}}y generalize,
Kahlig Peter, Matkowski Janusz
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Pseudo almost periodic solutions for a class of differential equation with delays depending on state
Advances in Nonlinear Analysis, 2019 In this paper, the exponential dichotomy, and Tikhonov and Banach fixed point theorems are used to study the existence and uniqueness of pseudo almost periodic solutions of a class of iterative functional differential equations of the ...
Zhao Hou Yu
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Faà di Bruno′s formula and nonhyperbolic fixed points of one‐dimensional maps
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 29, Page 1543-1549, 2004., 2004 Fixed‐point theory of one‐dimensional maps of ℝ does not completely address the issue of nonhyperbolic fixed points. This note generalizes the existing tests to completely classify all such fixed points. To do this, a family of operators are exhibited that are analogous to generalizations of the Schwarzian derivative. In addition, a family of functions
Vadim Ponomarenko
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Conditions for the oscillation of solutions of iterative equations
Abstract and Applied Analysis, Volume 2004, Issue 7, Page 543-550, 2004., 2004 We give some oscillation criteria for linear iterative functional equations. We compare obtained theorems with known results. We give applications to discrete equations too.
Wiesława Nowakowska +1 more
wiley +1 more source
Dynamics of Newton′s functions of Barna′s polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 2, Page 79-84, 2002., 2002 We define Barna′s polynomials as real polynomials with all real roots of which at least four are distinct. In this paper, we study the dynamics of Newton′s functions of such polynomials. We also give the upper and lower bounds of the Hausdorff dimension of exceptional sets of these Newton′s functions.
Piyapong Niamsup
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On local properties of compactly supported solutions of the two‐coefficient dilation equation
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 3, Page 139-148, 2002., 2002 Let a and b be reals. We consider the compactly supported solutions φ : ℝ → ℝ of the two‐coefficient dilation equation φ(x) = aφ(2x) + bφ(2x − 1). In this paper, we determine sets Ba,b, Ca,b, and Za,b defined in the following way: let x ∈ [0, 1]. We say that x ∈ Ba,b (resp., x ∈ Ca,b, x ∈ Za,b) if the zero function is the only compactly supported ...
Janusz Morawiec
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Dynamics of a certain sequence of powers
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 4, Page 283-288, 2000., 2000 For any nonzero complex number z we define a sequence a1(z) = z, a2(z)=za1(z),…,an+1(z)=zan(z), n ∈ ℕ. We attempt to describe the set of these z for which the sequence {an(z)} is convergent. While it is almost impossible to characterize this convergence set in the complex plane 𝒞, we achieved it for positive reals.
Roman Sznajder, Kanchan Basnyat
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