KAM Theorem and Renormalization Group [PDF]
arXiv, 2007 We give an elementary proof of the analytic KAM theorem by reducing it to a Picard iteration of a PDE with quadratic nonlinearity, the so called Polchinski renormalization group equation studied in quantum field theory.
arxiv
Genericity of Caustics and Wavefronts on an r-corner [PDF]
arXiv, 2009 We investigate genericities of reticular Lagrangian maps and reticular Legendrian maps in order to give generic classifications of caustics and wavefronts generated by a hypersurface germ without or with a boundary in a smooth manifold.
arxiv
Bifurcations of Wavefronts on an r-corner II: Semi-local classification [PDF]
arXiv, 2009 We give a classification of generic bifurcations of intersections of wavefronts generated by different points of a hypersurface with or without boundaries.
arxiv
Escaping orbits are also rare in the almost periodic Fermi-Ulam ping-pong [PDF]
arXiv, 2019 We study the one-dimensional Fermi-Ulam ping-pong problem with a Bohr almost periodic forcing function and show that the set of initial condition leading to escaping orbits typically has Lebesgue measure zero.
arxiv
KAM tori are no more than sticky [PDF]
arXiv, 2018 When a Gevrey smooth perturbation is applied to a quasi-convex integrable Hamiltonian, it is known that the KAM invariant tori that survive are sticky, that is, doubly exponentially stable. We show by examples the optimality of this effective stability.
arxiv
An Equivariant Liapunov Stability Test and the Energy-Momentum-Casimir Method [PDF]
arXiv, 2001 We present an equivariant Liapunov stability criterion for dynamical systems with symmetry. This result yields a simple proof of the energy-momentum-Casimir stability analysis of relative equilibria of equivariant Hamiltonian systems.
arxiv
Boundedness of solutions for a class of impact oscillators with time-denpendent polynomial potentials [PDF]
arXiv, 2013 In this paper, we consider the boundedness of solutions for a class of impact oscillators $$ \{{array}{ll} \displaystyle \ddot{x}+x^{2n+1}+\sum_{i=0}^{2n}p_{i}(t)x^{i}=0,& \quad {\rm for}\quad x(t)> 0, x(t)\geq 0,& \dot{x}(t_{0}^{+})=-\dot{x}(t_{0}^{-}),& \quad {\rm if}\quad x(t_{0})=0, {array}.
arxiv
Limit cycles by FEM for a one - parameter dynamical system associated to the Luo - Rudy I model
, 2011 An one - parameter dynamical system is associated to the mathematical problem governing the membrane excitability of a ventricular cardiomyocyte, according to the Luo-Rudy I model. Limit cycles are described by the solutions of an extended system.
Amuzescu, Bogdan +7 more
core
Gauge Fixing Invariance and Anti-BRST Symmetry [PDF]
arXiv, 2016 It is shown that anti-BRST invariance in quantum gauge theories can be considered as the quantized version of the symmetry of classical gauge theories with respect to different gauge fixing mechanisms.
arxiv
Linear stability of the elliptic relative equilibrium with $(1 +n)$-gon central configurations in planar $n$-body problem [PDF]
, 2019 We study the linear stability of $(1+n)$-gon elliptic relative equilibrium (ERE for short), that is the Kepler homographic solution with the $(1+n)$-gon central configurations. We show that for $n\geq 8$ and any eccentricity $e\in[0,1)$, the $(1+n)$-gon ERE is stable when the central mass $m$ is large enough.
arxiv +1 more source