The University of Western Australia
Professor Luchezar Stoyanov
Professor
Contact details
| Address | School of Mathematics and Statistics The University of Western Australia (M019) 35 Stirling Highway CRAWLEY WA 6009 Australia |
|---|---|
| Phone | 6488 3393 |
| Fax | 6488 1028 |
| stoyanov@maths.uwa.edu.au | |
| Personal homepage | http://www.maths.uwa.edu.au/~stoyanov |
Location
Room 1.09, Mathematics Building, Crawley campus
Key research
- Analysis,
- Geometry,
- Topology
Major research interests
- Dynamical systems
- Functional analysis
- Geometry
- Spectral and scattering theory
Qualifications
MSc Sofia, PhD DSc Bulgarian Acad.Sc.
Publications
Books
1. (with D.Dikranjan and Iv.Prodanov) Topological Groups: Characters, Dualities and Minimal Group Topologies. Marcel Dekker, New York, 1989.
2. (with V. Petkov) Geometry of reflecting rays and inverse spectral problems. John Wiley and Sons, Chichester, 1992.
3. (with Titu Andreescu and Oleg Mushkarov) Geometric Problems on Maxima and Minima, Birkh\"auser, Boston 2006.
Articles
4. A property of precompact minimal abelian groups. Annuaire Univ. Sofia Fac. Math. Mec. {\bf 70} (1975/76), 253-260.
5. Precompactness of the minimal metrizable periodic abelain groups. Annuaire Univ. Sofia Fac. Math. Mec. 71 (1976/77), part II, 45-52.
6. (with D. Dikranjan) A-classes of minimal abelian groups. Annuaire Univ. Sofia Fac. Math. Mec. 71 (1976/77), part II, 53-62.
7. Weak periodicity and minimality of topological groups. Annuaire Univ. Sofia Fac. Math. Mec. 73 (1978/79), 155-167.
8. Some minimal abelian groups are precompact. C. R. Acad. Bulgare Sci. 34 (1981), 473-475.
9. (with D. Dikranjan) Criterion for minimality of all subgroups of a topological abelian group. C. R. Acad. Bulgare Sci. 34 (1981), 635-638.
10. Some minimal abelain groups are precompact. PLISKA Stud. Math. Bulgar. 6 (1983), 75-89.
11. Dualities over compact commutative rings. Rend. Acad. Naz. XL, V Ser. 101 (1983), 155-176.
12. (with Yu. M. Smirnov) On minimal equivariant compact extensions. C. R. Acad. Bulgare Sci. 36 (1983), 733-736.
13. On the infinite-dimensional unitary groups, C. R. Acad. Bulgare Sci. 36 (1983), 1261-1263.
14. (with Iv. Prodanov) Minimal group topologies. Colloq. Math. Soc. Janos Bolyai 41. Topology and Appl., North-Holland, 1983, 493-508.
15. Total minimality of the unitary groups. Math. Z. 187 (1984), 273-283.
16. (with Iv. Prodanov) Every minimal abelain group is precompact. C.R.Acad. Bulgare Sci. 37 (1984), 23-26.
17. (with V. Petkov) Periodic geodesics of generic nonconvex domains in R^2 and the Poisson relation.} Bull. Amer. Math. Soc. 15 (1986), 88--90.
18. Generic properties of scattered rays. C.R.Acad. Bulgare Sci. 39 (1986), 13-14.
19. (with V. Petkov) Periods of multiple reflecting geodesics and inverse spectral results. Amer. J. Math. 109 (1987), 619--668.
20. Generic properties of periodic reflecting rays. Ergodic Theory and Dynam. Sys. 7 (1987), 597--609.
21. (with V. Petkov) Spectrum of the Poincar\'e map for periodic reflecting rays in generic domains. Math. Z. 194 (1987), 505--518.
22. Uniqueness of the topological entropy for endomorphisms on compact groups. Bolletino U.M.I. (7) 1-B (1987), 829-847.
23. (with D. Remus) On the completion of topological groups. C. R. Acad. Bulgare Sci. 40 (1987), 9-11.
24. Generic properties of periodic billiard trajectories (in Russian) Uspehi Mat. Nauk 42 (1987), 199-200.
25. (with V. Petkov) On the number of periodic reflecting rays in generic domains. Ergodic Theory and Dynam. Sys. 8 (1988), 81--91.
26. (with V. Petkov) Singularities of the scattering kernel and scattering invariants for several strictly convex obstacles. Trans. Amer. Math. Soc. 312 (1989), 203--235.
27. (with V. Petkov) :Singularities of the scattering kernel for a class of star-shaped non-convex obstacles. Mat. Apl. Comput. 8 (1989), 167--176.
28. An estimate from above of the number of periodic orbits for semi--dispersed billiards. Commun. Math. Physics 124 (1989), 217--227.
29. (with F. Cardoso and V. Petkov) Singularities of the scattering kernel for generic obstacles, Ann. Inst. Henri Poincar\'{e} 53, No. 4 (1990), 445--466.
30. A bumpy metric theorem and the Poisson relation for generic strictly convex domains. Math. Ann. 287 (1990), 675--696.
31. (with D. Remus) Complete minimal and totally minimal groups. Topology and Appl. 42 (1991), 57-69.
32. Nonexistence of generalized scattering rays and singularities of the scattering kernel for generic domains in R^3 Proc. Amer. Math. Soc. 113 (1991), 847-856.
33. Note on the periodic points of the billiard. J. Diff. Geometry 34 (1991), 835-837.
34. (with F. Takens) Generic properties of closed geodesics on smooth hypersurfaces. Math. Ann 296 (1993), 385-402.
35. (with V.Petkov) Sojourn times of trapping rays and the behaviour of the modified resolvent of the Laplacian. Ann. Inst. Henri Poincar\'{e} (Phys. Theorique) 62 (1995), 17-45.
36. (with K.H.Hofmann) Topological entropy for group and semigroup actions. Advances in Mathematics 115 (1995), 54-98.
37. Weak H\"older continuity of the generalized Hamiltonian flow. J. Math. Anal. Appl. 204 (1996), 164-182.
38. (with V. Petkov) Singularities of the scattering kernel for trapping obstacles, Ann. Sci. Ec. Norm. Sup. 29 (1996), 737-756.
39. On the scattering length spectrum, C.R.Acad.Sci Paris I, 325 (1997), 1169-1174.
40. Instability and entropy for a class of dispersing billiards, C.R.Acad.Sci.Paris I, 326 (1998), 737-742.
41. Exponential instability for a class of dispersing billiards, Ergod. Th. \& Dynam. Sys. 19 (1999), 1-26.
42. Generalized Hamiltonian flow and the Poisson relation for the scattering kernel, Ann. Scient. \'Ec. Norm. Sup. 33 (2000), 361-382.
43. On the scattering length spectrum for real analytic obstacles, J. Funct. Analysis 177 (2000), 459-488.
44. Spectrum of the Ruelle operator and exponential decay of correlations for open billiard flows, Amer. J. Math. 123 (2001), 715-759.
45. Rigidity of the scattering length spectrum, Math. Ann. 324 (2002), 743 - 771.
46. A sharp asymptotic for billiard travelling times in the exterior of two convex domains, Asymptotic Analysis 35 (2003), 235-255.
47. On the Ruelle-Perron-Frobenius theorem, Asymptotic Analysis 43 (2005), 131-150.
48. Scattering resonances for several small convex bodies and the Lax-Phillips conjecture, Memoirs of the American Mathematical Society, to appear.
49. Spectra of Ruelle transfer operators for contact flows, Serdica Math. J. 34 (2008), 219-252.
Conference Publications
50. Cardinalities of minimal abelian groups, Proc. 10th Spring Conference of Bulgarian Mathematicians, Sunny Beach (1981), 203 - 208.
51. On products of minimal and totally minimal groups, Proc. 11th Spring Conference of Bulgarian Mathematicians, Sunny Beach (1982), 287-294.
52. (with V. Petkov) Proprietes generiques de l'application de Poincare et des geodesiques periodiques generalisees. Seminaire Equations aux Derivees Partieles, Ecole Polytechnique, Centre de Math., Expose XI (1985-1986).
53. (with V. Petkov) Singularities of the scattering kernel for nonconvex obstacles. Conference Equations aux Derivees Partielles. Saint-Jean-de-Monts, Societe Math. de France (1987), Expose XI.
54. Generic properties of periodic reflecting rays and the Poisson relation, Proc. Banach Semester on Ergodic Theory and Dynamical Systems, Warsaw, 1986; PWN - Warszawa, 1989.
55. Regularity properties of the generalized Hamiltonian flow, S\'eminaire Equations aux Derivees Partielles, Ecole Polytechnique, Expos\'e VI, 1992-1993.
56. Poisson relation for the scattering kernel and inverse scattering by obstacles, Ecole Polytechnique, S\'eminaire Equations aux Derivees Partielles, Expos\'e V, 1994-1995.
57. (with V. Petkov) Sojourn times of reflecting rays and singularities of the scattering kernel, Proc. of Third International Conference on Mathematical and Numerical Aspects of Wave Propagation Phenomena, April 1995, Mandilieu, France, Ed. Gary Cohen, SIAM, Philadelphia, 1995, pp. 516-525.
58. Spectrum of the Ruelle operator and zeta functions for broken geodesic flows, Proc. Nat. Res. Symp. on Geometric Analysis and Applications, Australian National University, June 2000, pp. 201-212.
Other Publications
59. (with E. Stoyanova) The winter mathematical holidays in Bulgaria, Mathematics Competitions, J. of the World Federation of National Math. Competitions 2 (1989).
60. (with O. Mushkarov) Extremal Problems in Geometry (in Bulgarian). Enrichment Courses in Mathematics and Informatics, Narodna Prosveta, Sofia 1989 (133 pages).
1. (with D.Dikranjan and Iv.Prodanov) Topological Groups: Characters, Dualities and Minimal Group Topologies. Marcel Dekker, New York, 1989.
2. (with V. Petkov) Geometry of reflecting rays and inverse spectral problems. John Wiley and Sons, Chichester, 1992.
3. (with Titu Andreescu and Oleg Mushkarov) Geometric Problems on Maxima and Minima, Birkh\"auser, Boston 2006.
Articles
4. A property of precompact minimal abelian groups. Annuaire Univ. Sofia Fac. Math. Mec. {\bf 70} (1975/76), 253-260.
5. Precompactness of the minimal metrizable periodic abelain groups. Annuaire Univ. Sofia Fac. Math. Mec. 71 (1976/77), part II, 45-52.
6. (with D. Dikranjan) A-classes of minimal abelian groups. Annuaire Univ. Sofia Fac. Math. Mec. 71 (1976/77), part II, 53-62.
7. Weak periodicity and minimality of topological groups. Annuaire Univ. Sofia Fac. Math. Mec. 73 (1978/79), 155-167.
8. Some minimal abelian groups are precompact. C. R. Acad. Bulgare Sci. 34 (1981), 473-475.
9. (with D. Dikranjan) Criterion for minimality of all subgroups of a topological abelian group. C. R. Acad. Bulgare Sci. 34 (1981), 635-638.
10. Some minimal abelain groups are precompact. PLISKA Stud. Math. Bulgar. 6 (1983), 75-89.
11. Dualities over compact commutative rings. Rend. Acad. Naz. XL, V Ser. 101 (1983), 155-176.
12. (with Yu. M. Smirnov) On minimal equivariant compact extensions. C. R. Acad. Bulgare Sci. 36 (1983), 733-736.
13. On the infinite-dimensional unitary groups, C. R. Acad. Bulgare Sci. 36 (1983), 1261-1263.
14. (with Iv. Prodanov) Minimal group topologies. Colloq. Math. Soc. Janos Bolyai 41. Topology and Appl., North-Holland, 1983, 493-508.
15. Total minimality of the unitary groups. Math. Z. 187 (1984), 273-283.
16. (with Iv. Prodanov) Every minimal abelain group is precompact. C.R.Acad. Bulgare Sci. 37 (1984), 23-26.
17. (with V. Petkov) Periodic geodesics of generic nonconvex domains in R^2 and the Poisson relation.} Bull. Amer. Math. Soc. 15 (1986), 88--90.
18. Generic properties of scattered rays. C.R.Acad. Bulgare Sci. 39 (1986), 13-14.
19. (with V. Petkov) Periods of multiple reflecting geodesics and inverse spectral results. Amer. J. Math. 109 (1987), 619--668.
20. Generic properties of periodic reflecting rays. Ergodic Theory and Dynam. Sys. 7 (1987), 597--609.
21. (with V. Petkov) Spectrum of the Poincar\'e map for periodic reflecting rays in generic domains. Math. Z. 194 (1987), 505--518.
22. Uniqueness of the topological entropy for endomorphisms on compact groups. Bolletino U.M.I. (7) 1-B (1987), 829-847.
23. (with D. Remus) On the completion of topological groups. C. R. Acad. Bulgare Sci. 40 (1987), 9-11.
24. Generic properties of periodic billiard trajectories (in Russian) Uspehi Mat. Nauk 42 (1987), 199-200.
25. (with V. Petkov) On the number of periodic reflecting rays in generic domains. Ergodic Theory and Dynam. Sys. 8 (1988), 81--91.
26. (with V. Petkov) Singularities of the scattering kernel and scattering invariants for several strictly convex obstacles. Trans. Amer. Math. Soc. 312 (1989), 203--235.
27. (with V. Petkov) :Singularities of the scattering kernel for a class of star-shaped non-convex obstacles. Mat. Apl. Comput. 8 (1989), 167--176.
28. An estimate from above of the number of periodic orbits for semi--dispersed billiards. Commun. Math. Physics 124 (1989), 217--227.
29. (with F. Cardoso and V. Petkov) Singularities of the scattering kernel for generic obstacles, Ann. Inst. Henri Poincar\'{e} 53, No. 4 (1990), 445--466.
30. A bumpy metric theorem and the Poisson relation for generic strictly convex domains. Math. Ann. 287 (1990), 675--696.
31. (with D. Remus) Complete minimal and totally minimal groups. Topology and Appl. 42 (1991), 57-69.
32. Nonexistence of generalized scattering rays and singularities of the scattering kernel for generic domains in R^3 Proc. Amer. Math. Soc. 113 (1991), 847-856.
33. Note on the periodic points of the billiard. J. Diff. Geometry 34 (1991), 835-837.
34. (with F. Takens) Generic properties of closed geodesics on smooth hypersurfaces. Math. Ann 296 (1993), 385-402.
35. (with V.Petkov) Sojourn times of trapping rays and the behaviour of the modified resolvent of the Laplacian. Ann. Inst. Henri Poincar\'{e} (Phys. Theorique) 62 (1995), 17-45.
36. (with K.H.Hofmann) Topological entropy for group and semigroup actions. Advances in Mathematics 115 (1995), 54-98.
37. Weak H\"older continuity of the generalized Hamiltonian flow. J. Math. Anal. Appl. 204 (1996), 164-182.
38. (with V. Petkov) Singularities of the scattering kernel for trapping obstacles, Ann. Sci. Ec. Norm. Sup. 29 (1996), 737-756.
39. On the scattering length spectrum, C.R.Acad.Sci Paris I, 325 (1997), 1169-1174.
40. Instability and entropy for a class of dispersing billiards, C.R.Acad.Sci.Paris I, 326 (1998), 737-742.
41. Exponential instability for a class of dispersing billiards, Ergod. Th. \& Dynam. Sys. 19 (1999), 1-26.
42. Generalized Hamiltonian flow and the Poisson relation for the scattering kernel, Ann. Scient. \'Ec. Norm. Sup. 33 (2000), 361-382.
43. On the scattering length spectrum for real analytic obstacles, J. Funct. Analysis 177 (2000), 459-488.
44. Spectrum of the Ruelle operator and exponential decay of correlations for open billiard flows, Amer. J. Math. 123 (2001), 715-759.
45. Rigidity of the scattering length spectrum, Math. Ann. 324 (2002), 743 - 771.
46. A sharp asymptotic for billiard travelling times in the exterior of two convex domains, Asymptotic Analysis 35 (2003), 235-255.
47. On the Ruelle-Perron-Frobenius theorem, Asymptotic Analysis 43 (2005), 131-150.
48. Scattering resonances for several small convex bodies and the Lax-Phillips conjecture, Memoirs of the American Mathematical Society, to appear.
49. Spectra of Ruelle transfer operators for contact flows, Serdica Math. J. 34 (2008), 219-252.
Conference Publications
50. Cardinalities of minimal abelian groups, Proc. 10th Spring Conference of Bulgarian Mathematicians, Sunny Beach (1981), 203 - 208.
51. On products of minimal and totally minimal groups, Proc. 11th Spring Conference of Bulgarian Mathematicians, Sunny Beach (1982), 287-294.
52. (with V. Petkov) Proprietes generiques de l'application de Poincare et des geodesiques periodiques generalisees. Seminaire Equations aux Derivees Partieles, Ecole Polytechnique, Centre de Math., Expose XI (1985-1986).
53. (with V. Petkov) Singularities of the scattering kernel for nonconvex obstacles. Conference Equations aux Derivees Partielles. Saint-Jean-de-Monts, Societe Math. de France (1987), Expose XI.
54. Generic properties of periodic reflecting rays and the Poisson relation, Proc. Banach Semester on Ergodic Theory and Dynamical Systems, Warsaw, 1986; PWN - Warszawa, 1989.
55. Regularity properties of the generalized Hamiltonian flow, S\'eminaire Equations aux Derivees Partielles, Ecole Polytechnique, Expos\'e VI, 1992-1993.
56. Poisson relation for the scattering kernel and inverse scattering by obstacles, Ecole Polytechnique, S\'eminaire Equations aux Derivees Partielles, Expos\'e V, 1994-1995.
57. (with V. Petkov) Sojourn times of reflecting rays and singularities of the scattering kernel, Proc. of Third International Conference on Mathematical and Numerical Aspects of Wave Propagation Phenomena, April 1995, Mandilieu, France, Ed. Gary Cohen, SIAM, Philadelphia, 1995, pp. 516-525.
58. Spectrum of the Ruelle operator and zeta functions for broken geodesic flows, Proc. Nat. Res. Symp. on Geometric Analysis and Applications, Australian National University, June 2000, pp. 201-212.
Other Publications
59. (with E. Stoyanova) The winter mathematical holidays in Bulgaria, Mathematics Competitions, J. of the World Federation of National Math. Competitions 2 (1989).
60. (with O. Mushkarov) Extremal Problems in Geometry (in Bulgarian). Enrichment Courses in Mathematics and Informatics, Narodna Prosveta, Sofia 1989 (133 pages).
Research profile
