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Arnold diffusion in arbitrary degrees of freedom and crumpled 3-dimensional normally hyperbolic invariant cylinders
Arnold diffusion arbitrary degrees of freedom crumpled 3-dimensional hyperbolic invariant cylinders
2015/9/25
Arnold diffusion in arbitrary degrees of freedom and crumpled 3-dimensional normally hyperbolic invariant cylinders.
A digital model of coupled oscillators
Coupled oscillators Synchronization Digital oscillator
2015/8/27
A new model of coupled oscillators is proposed and investigated. All phase variables and parameters are integer-valued. The model is shown to exhibit two types of motions, those which involve periodic...
Hopf Bifurcations in Two-Player Delayed Replicator Dynamics
Hopf Bifurcations Two-Player Delayed Replicator Dynamics
2015/8/26
We investigate the dynamics of two-strategy replicator equa-tions in which competition between strategies is delayed by a given time interval T. Taking T as a bifurcation parameter, we demonstrate the...
Hopf Bifurcations in Delayed Rock–Paper–Scissors Replicator Dynamics
Replicator Delay Hopf bifurcation Limit cycle Lindstedt
2015/8/26
We investigate the dynamics of three-strategy (rock–paper–scissors) replicator equations in which the fitness of each strategy is a function of the population frequencies delayed by a time interval T....
A PROOF OF THE UNIFORMIZATION THEOREM FOR ARBITRARY PLANE DOMAINS
UNIFORMIZATION THEOREM ARBITRARY PLANE DOMAINS
2015/8/26
We present a simple constructive proof of the Uniformization Theorem which works for plane domains. The proof is a combination of covering space theory and Koebe's constructive proof of the Riemann ma...
The Forced Damped Pendulum:Chaos,Complication and Control
Forced Damped Pendulum Chaos Complication Control
2015/8/26
This paper will show that a “simple” differential equation modeling a garden-variety damped forced pendulum can exhibit extraordinarily complicated and unstable behavior.While instability and control ...
A Fatou–Bieberbach domain avoiding a neighborhood of a variety of codimension 2
Fatou–Bieberbach domain avoiding codimension 2
2015/8/26
A Fatou–Bieberbach domain avoiding a neighborhood of a variety of codimension 2.
Linked Solenoid Mappings and the Non-Transversality Locus Invariant
Solenoid Mappings Non-Transversality Locus Invariant
2015/8/26
Linked Solenoid Mappings and the Non-Transversality Locus Invariant.
In this paper we will give a proof of Kolmogorov’s theorem on the conservation of invariant tori. This proof is close to the one given by Bennettin, Galgani, Giorgilli and Strelcyn in [2]; we follow t...
PARAMETRIZING UNSTABLE AND VERY UNSTABLE MANIFOLDS
PARAMETRIZING UNSTABLE VERY UNSTABLE MANIFOLDS
2015/8/26
PARAMETRIZING UNSTABLE AND VERY UNSTABLE MANIFOLDS.
The KAM Theorem
KAM Theorem
2015/8/26
I first heard about the KAM theorem when I was an undergraduate, around 1966. It seemed to me the most beautiful result in the world, but for many years my interests were engaged elsewhere. Around 198...
A Compactification of H′ enon Mappings in C2 as Dynamical Systems
H′ enon Mappings C2 as Dynamical Systems
2015/8/26
A Compactification of H′ enon Mappings in C2 as Dynamical Systems.
Investigating the multimodality of multivariate data with principal curves
Multimodality Principal curves
2015/8/20
We propose a simple method to assess the number of subpopulations in multivariate data
by projecting the data on its principal curve and then applying Silverman’s bandwidth test
to the resulting uni...
CONTINUOUS COLORINGS ASSOCIATED WITH CERTAIN CHARACTERISTICS OF THE CONTINUUM
CONTINUOUS COLORINGS ASSOCIATED CERTAIN CHARACTERISTICS
2015/8/17
A coloring c:[X]n → Z is said to be irreducible if for every Y; X of equal cardinality c00[Y ]n = Z. The focus of this note will be to show that there are continuous irreducible colorings on sets of r...
Open colorings,the continuum and the second uncountable cardinal
Open colorings the continuum second uncountable cardinal
2015/8/17
The purpose of this article is to analyze the cardinality of the continuum using Ramsey theoretic statements about open colorings or “open coloring axioms.” In particular I will show that the conjunct...