On Lower Dimensional Invariant Toriin C^d Reversible Systems

In this paper, a result on the persistence of lower dimensional invariant tori in Cd reversible systems is obtained under some conditions. The theorem is proved for any d which is larger than some constants.

BOUNDEDNESS OF SOLUTIONS FOR SUPERLINEAR REVERSIBLE SYSTEMS

This paper is concerned with the boundedness of solutions for second order differential equations x + f(x, t)x + g(x, t) = 0, which are neither dissipative nor conservative, and where the functions f and g are odd in x and even in t, which are 1-periodic in t, and the function g satisfies g(x,t/x+, as|x| - +. Using the KAM theory for reversible systems, the author proves the existence of invariant tori and thus the boundedness of all the solutions and the existence of quasiperiodic solutions and subharmonic solutions.

Boundedness of solutions for sublinear reversible systems

We are concerned with the boundedness of all the solutions for second order differential equation $$\ddot x + f\left( x \right)\dot x + g\left( x \right) = e\left( t \right),$$ , wheref(x) andg(x) are odd, e( t) is odd and 1-periodic, andg(x) satisfies $$Sign \left( x \right) \cdot g\left( x \right) \to + \infty ,\frac{{g\left( x \right)}}{x} \to 0,as\left| x \right| \to + \infty .$$

Reverse genetics systems for SARS-CoV-2:Development and applications

The recent emergence of severe acute respiratory syndrome coronavirus 2(SARS-CoV-2)caused serious harm to human health and struck a blow to global economic development.Research on SARS-CoV-2 has greatly benefited from the use of reverse genetics systems,which have been established to artificially manipulate the viral genome,generating recombinant and reporter infectious viruses or biosafety level 2(BSL-2)-adapted non-infectious replicons with desired modifications.These tools have been instrumental in studying the molecular biological characteristics of the virus,investigating antiviral therapeutics,and facilitating the development of attenuated vaccine candidates.Here,we review the construction strategies,development,and applications of reverse genetics systems for SARS-CoV-2,which may be applied to other CoVs as well.

Limit Cycles Bifurcating from a Quadratic Reversible Lotka-Volterra System with a Center and Three Saddles

This paper is concerned with limit cycles which bifurcate from a period annulus of a quadratic reversible Lotka-Volterra system with sextic orbits.The authors apply the property of an extended complete Chebyshev system and prove that the cyclicity of the period annulus under quadratic perturbations is equal to two.

Brake Orbits of a Reversible Even Hamiltonian System Near an Equilibrium

In this paper,we consider the brake orbits of a reversible even Hamiltonian system near an equilibrium.Let the Hamiltonian system(H S)x=J H(x)satisfies H(0)=0,H(0)=0,reversible and even conditions H(Nx)=H(x)and H(-x)=H(x)for all x∈R^(2n).Suppose the quadratic form Q(x)=1/2 is non-degenerate.Fixτ_(0)>0 and assume that R^(2n)=E⊕F decomposes into linear subspaces E and F which are invariant under the flow associated to the linear system x=J H''(0)x and such that each solution of the above linear system in E isτ_(0)-periodic whereas no solution in F{0}isτ_(0)-periodic.Writeσ(τ_(0))=σ_Q(τ_(0))for the signature of Q|E.Ifσ(τ_(0))≠=0,we prove that either there exists a sequence of brake orbits x_k→0 withτk-periodic on the hypersurface H^(-1)(0)whereτ_k→τ_(0);or for eachλclose to 0 withλ_(σ)(τ_(0))>0 the hypersurface H-1(λ)contains at least 1/2|σ(τ_(0))|distinct brake orbits of the Hamiltonian system(HS)near 0 with periods nearτ_(0).Such result for periodic solutions was proved by Bartsch in 1997.

KAM Theory for Partial Differential Equations

In the last years much progress has been achieved in KAM theory concerning bifurcation of quasi-periodic solutions of Hamiltonian or reversible partial differential equations.We provide an overview of the state of the art in this field.