ATTRACTING BASINS OF VOLUME PRESERVING AUTOMORPHISMS OF ℂk

2008 ◽  
Vol 19 (07) ◽  
pp. 801-810 ◽  
Author(s):  
HAN PETERS ◽  
LIZ RAQUEL VIVAS ◽  
ERLEND FORNÆSS WOLD
Keyword(s):  
Fixed Point ◽  
Stable Manifold ◽  
The Other ◽  
Topological Properties ◽  
Attracting Set ◽  
Other Hand ◽  
Hyperbolic Fixed Point ◽  
Attracting Fixed Point ◽  
Volume Preserving

We study topological properties of attracting sets for automorphisms of ℂk. Our main result is that a generic volume preserving automorphism has a hyperbolic fixed point with a dense stable manifold. On the other hand, we show that an attracting set can only contain a neighborhood of the fixed point if it is an attracting fixed point. We will see that the latter does not hold in the non-autonomous setting.

scholarly journals Well-definedness and observational equivalence for inductive–coinductive programs

2019 ◽  
Vol 29 (4) ◽  
pp. 419-468
Author(s):  
Henning Basold ◽  
Helle Hvid Hansen
Keyword(s):  
Fixed Point ◽  
Modal Logic ◽  
The Other ◽  
Observational Equivalence ◽  
Other Hand ◽  
Inductive Types ◽  
Point Types ◽  
Usual Topology

Abstract We define notions of well-definedness and observational equivalence for programs of mixed inductive and coinductive types. These notions are defined by means of tests formulas which combine structural congruence for inductive types and modal logic for coinductive types. Tests also correspond to certain evaluation contexts. We define a program to be well-defined if it is strongly normalizing under all tests, and two programs are observationally equivalent if they satisfy the same tests. We show that observational equivalence is sufficiently coarse to ensure that least and greatest fixed point types are initial algebras and final coalgebras, respectively. This yields inductive and coinductive proof principles for reasoning about program behaviour. On the other hand, we argue that observational equivalence does not identify too many terms, by showing that tests induce a topology that, on streams, coincides with usual topology induced by the prefix metric. As one would expect, observational equivalence is, in general, undecidable, but in order to develop some practically useful heuristics we provide coinductive techniques for establishing observational normalization and observational equivalence, along with up-to techniques for enhancing these methods.

scholarly journals Consolidation via Tacit Culpability Measures: Between Explicit and Implicit Degrees of Culpability

2021 ◽  
Author(s):  
Jandson S. Ribeiro ◽  
Matthias Thimm
Keyword(s):  
Fixed Point ◽  
Knowledge Base ◽  
Special Class ◽  
Belief Change ◽  
Minimal Change ◽  
The Other ◽  
Preference Relations ◽  
Other Hand ◽  
The One ◽  
Rationality Postulates

Restoring consistency of a knowledge base, known as consolidation, should preserve as much information as possible of the original knowledge base. On the one hand, the field of belief change captures this principle of minimal change via rationality postulates. On the other hand, within the field of inconsistency measurement, culpability measures have been developed to assess how much a formula participates in making a knowledge base inconsistent. We look at culpability measures as a tool to disclose epistemic preference relations and build rational consolidation functions. We introduce tacit culpability measures that consider semantic counterparts between conflicting formulae, and we define a special class of these culpability measures based on a fixed-point characterisation: the stable tacit culpability measures. We show that the stable tacit culpability measures yield rational consolidation functions and that these are also the only culpability measures that yield rational consolidation functions.

scholarly journals Sturmian Sequences and Invertible Substitutions

2011 ◽  
Vol Vol. 13 no. 2 (Combinatorics) ◽  
Author(s):  
Li Peng ◽  
Bo Tan
Keyword(s):  
Fixed Point ◽  
The Other ◽  
Sturmian Sequence ◽  
Other Hand ◽  
Angle Alpha ◽  
International Audience ◽  
Sturmian Sequences ◽  
Irrational Angle

Combinatorics International audience It is known that a Sturmian sequence S can be defined as a coding of the orbit of rho (called the intercept of S) under a rotation of irrational angle alpha (called the slope). On the other hand, a fixed point of an invertible substitution is Sturmian. Naturally, there are two interrelated questions: (1) Given an invertible substitution, we know that its fixed point is Sturmian. What is the slope and intercept? (2) Which kind of Sturmian sequences can be fixed by certain non-trivial invertible substitutions? In this paper we give a unified treatment to the two questions. We remark that though the results are known, our proof is very elementary and concise.

Some Random Fixed Point Theorems and Comparing Random Operator Equations

2011 ◽  
Vol 52-54 ◽  
pp. 127-132
Author(s):  
Ning Chen ◽  
Bao Dan Tian ◽  
Ji Qian Chen
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Random Operator ◽  
The Other ◽  
Operator Equations ◽  
Random Solution ◽  
Random Fixed Point ◽  
Other Hand ◽  
The Common

In this paper, some new results are given for the common random solution for a class of random operator equations which generalize several results in [4], [5] and [6] in Banach space. On the other hand, Altman’s inequality is also extending into the type of the determinant form. And comparing some solution for several examples, main results are theorem 2.3, theorem 3.3-3.4, theorem 4.1 and theorem 4.3.

ON SOME GLOBAL BIFURCATIONS OF THE DOMAINS OF FEASIBLE TRAJECTORIES: AN ANALYSIS OF RECURRENCE EQUATIONS

2005 ◽  
Vol 15 (05) ◽  
pp. 1625-1639 ◽  
Author(s):  
EN-GUO GU ◽  
JIONG RUAN
Keyword(s):  
Fixed Point ◽  
Stable Manifold ◽  
The Other ◽  
Computer Assisted ◽  
Two Dimensional ◽  
Global Bifurcations ◽  
Basin Boundary ◽  
Recurrence Equations ◽  
Critical Curves ◽  
Global Properties

This paper is an attempt to give new results, by a computer-assisted study, on some global bifurcations that change the structure of the domain of feasible trajectories (bounded discrete trajectories having an ecological sense) which can be obtained by the union of all rank preimages of axes. Three two-dimensional recurrence equations (or maps) are analyzed. The two first maps are degenerated invertible maps (i.e. the inverses of them are well defined except a set of zero lebergue measure) for which the basins of attractor are obtained by the backward iteration of a stable manifold of a saddle fixed point belonging to the basin boundary, and the interior domains of feasible trajectories are given by the intersection between the basin of attractor and the first quadrant. The other is a noninvertible map which is investigated by the use of critical curves, a powerful tool for the analysis of global properties of two-dimensional maps.

scholarly journals The non-SUSY AdS6 and AdS7 fixed points are brane-jet unstable

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Minwoo Suh
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Decay Channel ◽  
Scalar Potential ◽  
The Other ◽  
Other Hand ◽  
Weak Gravity

Abstract In six- and seven-dimensional gauged supergravity, each scalar potential has one supersymmetric and one non-supersymmetric fixed points. The non-supersymmetric AdS7 fixed point is perturbatively unstable. On the other hand, the non-supersymmetric AdS6 fixed point is known to be perturbatively stable. In this note we examine the newly proposed non-perturbative decay channel, called brane-jet instabilities of the AdS6 and AdS7 vacua. We find that when they are uplifted to massive type IIA and eleven- dimensional supergravity, respectively, the non-supersymmetric AdS6 and AdS7 vacua are both brane-jet unstable, in fond of the weak gravity conjecture.

scholarly journals On the Costs of Classical Logic

Erkenntnis ◽  
2021 ◽  
Author(s):  
Luca Castaldo
Keyword(s):  
Fixed Point ◽  
Classical Logic ◽  
The Other ◽  
Theories Of Truth ◽  
Other Hand ◽  
Fixed Point Semantics ◽  
Theoretical Equivalence ◽  
The One

AbstractThis article compares classical (or -like) and nonclassical (or -like) axiomatisations of the fixed-point semantics developed by Kripke (J Philos 72(19): 690–716, 1975). Following the line of investigation of Halbach and Nicolai (J Philos Logic 47(2): 227–257, 2018), we do not compare and qua theories of truth simpliciter, but rather qua axiomatisations of the Kripkean conception of truth. We strengthen the central results of Halbach and Nicolai (2018) and Nicolai (Stud Log 106(1): 101–130, 2018), showing that, on the one hand, there is a stronger sense in which some variants of and some variants of can be taken to be, truth-theoretically, equivalent. On the other hand, we show that this truth-theoretical equivalence is not preserved by some other variants of and , arguing that the variants are more adequate axiomatisations of the fixed-point semantics than the corresponding variants.

On Saint Venant’s Principle: Elastic Shells and Plates

1960 ◽  
Vol 27 (3) ◽  
pp. 417-422 ◽  
Author(s):  
P. M. Naghdi
Keyword(s):  
Fixed Point ◽  
Integral Formula ◽  
Middle Surface ◽  
The Other ◽  
Elastic Shells ◽  
Partial Derivatives ◽  
Other Hand ◽  
Derivatives Of ◽  
Surface Loads

This investigation is concerned with an examination of the validity of Saint Venant’s principle in the theory of thin elastic shells and plates. With the aid of an integral formula derived for the displacements and their relevant partial derivatives of all orders at a fixed point of the shell middle surface, the conclusions reached may be roughly stated as follows: If the loads acting on the shell maintained in equilibrium are purely edge loads, then the orders of magnitude of the displacements and stresses are in accord with the traditional statement of Saint Venant’s principle. On the other hand, if the loads on the shell are purely surface loads, then the conclusions concerning the orders of magnitude of the displacements and stresses are the same as those of the modified Saint Venant principle.

scholarly journals Some Fixed Point Results for Perov-Ćirić-Prešić Type F-Contractions with Application

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Abdolsattar Gholidahneh ◽  
Shaban Sedghi ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Nonlinear Operator ◽  
The Other ◽  
Contractive Mappings ◽  
Other Hand ◽  
Operator Systems

Ćirić and Prešić developed the concept of Prešić contraction to Ćirić-Prešić type contractive mappings in the background of a metric space. On the other hand, Altun and Olgun introduced Perov type F-contractions. In this paper, we extend the concept of Ćirić-Prešić contractions to Perov-Ćirić-Prešić type F-contractions. Our results modify some known ones in the literature. To support our main result, an example and an application to nonlinear operator systems are presented.

Subcontinua of the closure of the unstable manifold at a homoclinic tangency

1999 ◽  
Vol 19 (2) ◽  
pp. 289-307 ◽  
Author(s):  
MARCY BARGE ◽  
BEVERLY DIAMOND
Keyword(s):  
Fixed Point ◽  
Unstable Manifold ◽  
Stable Manifold ◽  
Inverse Limit ◽  
Resonance Condition ◽  
Homoclinic Tangency ◽  
Limit Space ◽  
Open Set ◽  
Hyperbolic Fixed Point ◽  
Inverse Limit Space

Suppose that $F$ is a $C^\infty$ diffeomorphism of the plane with hyperbolic fixed point $p$ for which a branch of the unstable manifold, $W^u_+(p)$, has a same-sided quadratic tangency with the stable manifold, $W^s(p)$. If the eigenvalues of $DF$ at $p$ satisfy a non-resonance condition, each nonempty open set of $ \cl( W^u_+(p))$ contains a copy of any continuum that can be written as the inverse limit space of a sequence of unimodal bonding maps.

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