相关论文: The Pitchfork Bifurcation

Decision making is a fundamental capability of autonomous systems. As decision making is a process which happens over time, it can be well modeled by dynamical systems. Often, decisions are made on the basis of perceived values of the…

We give a new characterization of pseudoconvex point, and of finite type point, using analytic discs.

According to the Weinstein splitting theorem, any Poisson manifold is locally, near any given point, a product of a symplectic manifold with another Poisson manifold whose Poisson structure vanishes at the point. Similar splitting results…

The geometrical theory of partial differential equations in the absolute sense, without any additional structures, is developed. In particular the symmetries need not preserve the hierarchy of independent and dependent variables. The order…

We investigate the separability of arbitrary dimensional tripartite sys- tems. By introducing a new operator related to transformations on the subsystems a necessary condition for the separability of tripartite systems is presented.

We prove an abstract Nyquist criterion in a general set up. As applications, we recover various versions of the Nyquist criterion, some of which are new.

We use bifurcation theory to determine the existence of infinitely many new examples of triply periodic minimal surfaces in $\mathbb R^3$. These new examples form branches issuing from the H-family, the rPD-family, the tP-family, and the…

We prove an extension of one direction in Marty's theorem where the spherical derivative is replaced by a more general quantity involving higher derivatives.

This short article contains the construction of a construction that generalizes the concept of the derivative of a function of one variable, using the theory of filters. The paper presents a new concept, demonstrates that it really…

We modify an argument for multiparameter bifurcation of Fredholm maps by Fitzpatrick and Pejsachowicz to strengthen results on the topology of the bifurcation set. Furthermore, we discuss an application to families of differential equations…

This paper argues that, insofar as we doubt the bivalence of the Continuum Hypothesis or the truth of the Axiom of Choice, we should also doubt the consistency of third-order arithmetic, both the classical and intuitionistic versions.…

We obtain local and global bifurcation for periodic solutions of Hamiltonian systems by using a new way to apply a comparison principle of the spectral flow that was originally introduced by Pejsachowicz in a joint work with the third…

There exists a variety of physically interesting situations described by continuous maps that are nondifferentiable on some surface in phase space. Such systems exhibit novel types of bifurcations in which multiple coexisting attractors can…

In this paper, an interesting and new bifurcation phenomenon that limit cycles could be bifurcated from nilpotent node (focus) by changing its stability was investigated. It is different from lowing its multiplicity in order to get limit…

This is an introduction to the theory of disconjugacy for a second order linear differential equation. We give new proofs of some of basic results and obtain new sufficient conditions for disconjugacy (in particular, on the whole real…

Priestley duality has diverse applications in various branches of mathematics. In this survey, we discuss its usefulness in pointfree topology. This is done by providing Priestley perspective on several key notions, including spatiality,…

We derive a method for finding Lie Symmetries for third-order difference equations. We use these symmetries to reduce the order of the difference equations and hence obtain the solutions of some third-order difference equations. We also…

Symmetry is a common feature of many combinatorial problems. Unfortunately eliminating all symmetry from a problem is often computationally intractable. This paper argues that recent parameterized complexity results provide insight into…

The concepts of symmetry and its breakdown are investigated in two different terms according to whether the resulting asymmetry is universal or only obtained for a special configuration: we shall illustrate this by considering in the first…

This is the first part of a series devoting to the generalizations and applications of common theorems in variational bifurcation theory. Using parameterized versions of splitting theorems in Morse theory we generalize some famous…