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An important problem in smooth ergodic theory is to understand an
appearance of chaotic behavior in systems governed by deterministic
laws. Now it is understood that chaotic behavior is caused by th...
Note on the Number of Steady States for a 2D Smoluchowski Equation
the Number Steady States 2D Smoluchowski Equation
2014/4/4
Dynamics of concentrated polymer solutions are modeled by a Smoluchowski equation. At high concentrations, such solutions form liquid crystalline polymers of nematic structure. We prove that at high i...
Asymptotic stability of ground states in some Hamiltonian PDEs with symmetry
Asymptotic stability of ground states Hamiltonian PDEs symmetry
2011/9/22
Abstract: We consider a ground state (soliton) of a Hamiltonian PDE. We prove that if the soliton is orbitally stable then it is also asymptotically stable. The main assumptions are transversal nondeg...
Multiple steady states in a mathematical model for interactions between T cells and macrophages
mathematical model T cells and macrophages Cell Behavior
2011/10/9
Abstract: The aim of this paper is to prove results about the existence and stability of multiple steady states in a system of ordinary differential equations introduced by R. Lev Bar-Or to model the ...
Bernoulli equilibrium states for surface diffeomorphisms
Equilibrium measures Countable Markov partitions Bernoulli
2011/9/14
Abstract: Suppose f is a $C^{1+\alpha}$ surface diffeomorphism, and m is an equilibrium measure of a Holder continuous potential. We show that if m has positive metric entropy, then f is measure theor...
On resonances and bound states of the 't Hooft-Polyakov monopole
resonances bound states 't Hooft-Polyakov monopole
2011/3/3
We present a systematic approach to the linearised Yang-Mills-Higgs equations in the background of a 't Hooft-Polyakov monopole and use it to unify and extend previous studies of their spectral proper...